It's probably not worth rebuilding the wheel of it actually needs that.
I think if you're friendly the shop should be ok with doing the work, but there are mixed opinions on this.
Do look at upgrading the whole bike, though. It may not be worth it to keep the frame, particularly if you can sell the older built bike for a decent price.

What is the condition of the other parts on your current bike? Do you have fresh tires, a new bottom bracket, headset bearings, bar tape, and brake pads? Are your brake calipers and saddle in good condition? Is your front wheel hub, spokes and nipples in good shape? Do the brake surfaces on your rims have plenty of life left in them? Are you happy with the frame and fork your currently have?

If you answered yes to all of the above, then maybe it makes sense to just replace the shifters, derailleurs, chain, crankset, cassette and rear hub. But chances are that some of the things above on your current bike need to be changed out now or in the near future anyway...so just getting a new (or slighly used) bike may be a better overall investment. It also now gives you the option of having a back up bike, or just selling the old bike as is. Chances are nobody is going to buy your old 8 speed parts, and you'll have no use for them going forward.

Just like a car, not all the parts on a bike are not meant to last forever. When you consider doing major maintenance on an older car, you don't just pour money into it...you think of what else is up for repairs then you weigh your options on if you want to buy a new(er) car instead of pouring money into an older one. Also, just like cars, there are times where nostolgia of a given bike frame makes it worth it to pour money into it rather than buying something new.

Buy all of the new parts from an online store like Merlin Cycles and install them yourself.

I bought the bike new in Sept of last year, so it's less than a year old with about 500 miles on it total. I bought the bike because I love the flat black, as shallow as it may seem and probably is, it's the bike I "wanted" to ride, and it still is! Everything is in great shape and the 8 speed shifts great for what it is, but I find myself in between gears and constantly shifting. My plan was to keep the crankset as is for now and upgrade everything else. I thought (my rookie mistake) that upgrading bike parts was easy, I never idmagined it would be this difficult going from 8 to 11. Lesson learned I guess.

What is the distance between the frame's rear dropouts?

It's a disk brake, bike, right? If so, I would follow the bike shop's advice on this and sell the bike. Here's why...

You will need to replace the wheels, cassette, chain, derailleurs, crankset, and shifters. The new parts you will need will likely exceed the new price of the bike. And, if you cannot do the work yourself, the labor costs will add up. There is nothing wrong with doing a mega upgrade that exceeds the value of the bike-- I did that with my tri bike. But, it was more cost-effective for me, because I could easily do all the work and shop some parts cheaper in the used market.

If you do it yourself, go for it, and have fun learning about bike maintenance. But, if you will hand it all over to a bike shop to do it, consider buying the next level up Diverge with 11 speed going in. You might lose the favorite color, but you would be getting a very good bike overall without the upgrade costs and hassles. You can find some pretty amazing new-old-stock Diverge bikes on eBay for a lot less than new. A friend of mine got a carbon Diverge with 11-speed 105 on eBay for <<$2K and is thrilled.

Ahh...I assumed it was an older 8 speed bike you were referencing.

I'm not sure if you can use the chainrings on your current crankset for 11 speed though. The tooth pattern might be different, so I would at least confirm that.

Maybe another option is asking the LBS if they have an old 10 speed groupset that you could move to. There's a chance that your current rear hub, because it's fairly new, might be 8/9/10 speed compatible, so that's one major thing less to swap out. The difference in gears between 8 and 10 speed is pretty significant. 10 to 11 speed...not so much.

You would get a way better price on a 10 speed group from any of the UK online stores.

Thanks for the replays everyone. I'll check the crank and I'm fine with 10 speed as well. I was only going to go to 11 because I figured if I'm upgrading, it wouldn't hurt to be the newest release. It appears the hub on the wheels I have is built for an 11 speed. Just doing some googling at work and will need to confirm the spacers on my bike when I get home. The hub is 135x12 QR. I'm hoping I might just get lucky,(which never happens) swap cassettes and the rest of the upgrade becomes fairly straight forward. I'm planning on doing the work myself. Once I get everything figured out I'll do a tutorial of the upgrade and show everyone how NOT to do it! And review some beers as I go as well. I'll dig into it this weekend.

Honestly, your plan is just fine. It makes most sense (to me) to do the work yourself and treat it as a learning experience. If something gets screwed up, LBS's have plenty of stories of half-builds coming in from errant DIYers. You might get an eye-roll, but they'll take your money to build it right, if they're a decent shop.

On the hub: you likely won't find a replacement free-hub for those wheels, IF it's even possible to replace it. The shop might be able to source it, IF it exists. More likely, and if you want the shop to actually want to help you install the parts you bought elsewhere, I would suggest having them find you a moderately priced wheelset that can accommodate the 11-speed cogs. Yeah, you'd be able to find them online, as well, but, since the guy already knows your plan, call it an olive branch to keep them on your side. If you haven't already purchased them elsewhere, buy any new cables and housings, bar tape, etc. from the shop, too.

Highly dependent on the shop and their general clientele: Since you will have no use for the old wheels or parts, you could maybe see if they would take them as spares for other customers for some offset on the wheel cost. The more grease permanently tattooed on the hands of the mechanics, the more likely they are to do this for you.

I got a nice shimano group set and some training wheels from Merlin last year. It was high quality, well cared for stock that shipped quickly. Don't worry that it's coming from the UK. They do a great job serving US customers.
I had my local shop install and set it all up on my existing bike. I don't have the time, tools or skills to do it myself. I don't think they minded. They make most of their money on labor anyways and generally love working on bikes; esp setting up new components. That's my 2 cents.

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"The first virtue in a soldier is endurance of fatigue; courage is only the second virtue."
- Napoleon Bonaparte

I just did this, going from Sora/2200 groupset but to Tiagra since I wanted to keep 10speed rather than 11 speed (my 2nd bike is 10 spd dura-ace, so wanted to keep the parts compatible.)

It was a lot of fun (and work!) but eminently doable - I'm a near-complete bike noob so I had to buy ALL the tools and learn everything from scratch (youtube is awesome).

It also cost more than I expected, but a large chunk of those costs were the $300+ in tools I spent to do the upgrade. Yeah, that's right, it actually costed me nearly $300 in tools aside from the groupset to do it right, and that doesn't even include the price of a good bike stand. (The highly recommended Derailleur Hangar adjustment tool itself is $75+)

Also took a long time for me to get it right. Conceptually it's easy, and if you've done it before, if you're not working with internal cabling, you can swap out the entire FD/RD and recable it in under 30 minutes if your stuff is set up and ready to go.

It took me like 10 hours, no joke. Mainly because I would set it all up, realize I screwed something up , and have to re do the entire thing. I think I recabled my bike like 4 times and rewrapped the handlebar tape like 6 times before I got everything just right.

I did this a few months ago, going from an older Sora/Tiagra group to 105 11-speed. Everything was just buying parts and installing besides the wheel. I ended up buying a new hub and spokes, building the wheel up myself, then having my LBS dish and true it. Saved ~$100 vs buying a cheap 11-speed wheelset.

If you're even mildly curious about doing your own bike maintenance, I would highly suggest doing the labor yourself. Once you have all the parts and tools it should only take a weekend to build up if you are follow Youtube videos (what I did).

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Strava

Have you thought about just changing out the cassette? It's a lot easier and WAY cheaper. You should be able to buy a closer ratio 8 speed cassette plus a chain whip and a cassette lock removal tool for less than $50. Swapping is a 5 minute job, taking your time. A 13-26 would tighten up steps between gears considerably, and still leave you a reasonable amount of total range with the Diverge's 48/32 chainrings. How's the terrain where you typically ride? It's pretty flat here where I live. I put a 14-25 cassette on my Sora-equipped road bike with a 50/34T compact front crankset. It's very rare than I spin out the top gear or wish I had a lower bottom gear for climbing.

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"They're made of latex, not nitroglycerin"

It's pretty hilly here, a 20 mile ride can get you anywhere from 800 to 1800 ft in elevation. I always choose the harder routes because why not. The hills aren't all that long but you can get a 10-15% grade for a half mile on most of the hills climbing out of the valley. So I can spin out the 11 on the way in, but use the 32 on the way out. That's my thinking on upgrading to 10 or 11 speed to find that sweet gear like on my tri bike. I attached a pic of the rear spacing. It does appear to have a spacer, more experienced eyes can tell me if that needs to be there or is a spacer to accommodate the 8 speed cassette. I've contacted SunRace to find out the width of the 8 speed cassette compared to their 10 or 11 as well. This is the only part holding me back from starting this project. Side note, competitive cycling has a pretty decent sale on components right now.

With 10-15% grades, I can see why you need to keep the range. Biggest climb/descent in my county is 3-4% for less than a mile.

Can't see the attachment, but if you have a spacer with an 8 speed cassette, it's probably an 11 speed compatible freehub. There was no change on freehub width from 8-10; 9 speed cassette was the same width as 8, and 10 speed cassette was actually narrower so they used the same hub and a 1mm spacer. Not until they went to 11 did the freehub get wider. 8 and 9 speed cassettes work on an 11 speed freehub with a 1.8mm spacer. 10 speed works on an 11 speed freehub with 2.8mm of spacing (usually a combination of 1 and 1.8mm). I wouldn't be surprised if, for inventory simplification, Specialized didn't build all its 8/9/10 speed road bikes with 11 speed compatible freehub wheels anymore.

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"They're made of latex, not nitroglycerin"

So it may be possible to just switch the cassette from 8 to 11 (or 10). That makes sense because when I look up the wheels on specializeds site, it's a sealed, 3 pawl ratchet, 11 speed hub. If that's the case I can't wait to order the parts and get this started! The wheels are Axis 4.0 SCS QR.

I'll also warn that before you dive into this whole endeavor, know that the first thing you should probably check right now is your rear derailleur hangar alignment.

I know, sounds weird and obscure, and the tool that checks and repairs it from Park Tool costs $75+, but if your rear derailleur hangar is out of alignment (which sounds very possible to me, if not likely), you may spend a gob of money upgrading your whole drivetrain, and having the exact same problem plague you.

Wanna know how I know this? Did this exact same thing myself - swapped out the Sora/2200 8sp to full current-gen Tiagra 10sp, and STILL had RD shifting problems until I caved and bought the tool, which solved all my shifting problems instantly. I probably could have gotten back to perfect shifting on my 8sp with this tool alone (but I'm happy I upgraded despite this fact.)

Youtube has several great videos on the very-easy to use tool and the very-easy to do repair with the tool. Check it out for sure before you opt to spend hundreds on upgrading, as you'll likely need this tool regardless once you commit to the RD upgrade.

I have a 1996 or 1997ish vintage Specialozed TriSpoke with the old 8, 9, 10 sped compatible freehub. I put a Wheels Manufacturing Campy 11 speed conversion cassette on it and it works fine with any 11-speed group. So get a conversion cassette, shifters, and derailleurs and be happy. Should work.

Is it just me or is one of your chainlinks fucked, right in the middleline of the picture?

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-shoki

I thought the chain was messed up as well when I uploaded the pic last night. Went out to double check and they all look like that.

Ah, never seen that before. That special one in the close up looked weird from that angle though.

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-shoki

It sure looks like there is a spacer between the cassette and freehub body.

It sounds like you bought the bike for just the frame and not the components. Considering the original bike specs, going complete Ultegra 6800 is probably more than what you paid for the bike. If this were a "vintage" bike vs new, I would say keep it "vintage" and get a different bike. If you really love this frame, I wouldn't try to Frankenstein something together. Depending on your budget, I would build something that you will be happy with. Personally, I would just go the 10-speed route, since your current wheels will work with a 10-speed cassette (Shimano freehubs like the one you probably have work with 8-9-10 speed cassettes). The 10-speed will also give you the gearing you're looking for. You have a lot of options then (eg, Tiagra, 105, older Ultegra). Your crank will likely work with 10-speed, but I would look for a groupset that includes a crank/BB. From your photo, it looks like the bike has an older Octalink BB, which makes finding replacements harder.

Regarding the LBS, most of the ones I go to live in the 21st century and will happily install customer provided components. Sure they would prefer if you bought the stuff from them, but if they want to survive they'll be happy for your business anyway. If you have decent mechanical skills, this could also be a fun project to try yourself as well.

Good luck!

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"Most of my heroes don't appear on no stamps"
Blog = http://extrememomentum.com|Photos = http://wheelgoodphotos.com