Whenever I can't seem to get a derailleur (front or rear) to work right by "tweaking," I go back to the appropriate Park Tools YouTube video and follow the process start to finish. That usually does the trick.

If that doesn't work, I'd start looking for a cable kink or other obstruction.

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"They're made of latex, not nitroglycerin"

if you've swapped many times before with no issues, i'd wonder if it was something silly that you overlooked, like the wheel was crooked in the axle or not fully sat in the dropouts, or like said above, a cable kink or if something got bent that you didn't know about.

not the same situation, but i was swapping hollowtech ii cranks which ive done many times and for the life of me i couldn't get the crank arm fully seated on the crank shaft, and it drove me nuts for hours. i even posted on this forum for help. turns out one of the pinch bolts of the crank arm was screwed in too tight without me knowing. i loosened the bolt which was in front of my face the whole time and my problem was solved. lol. so hopefully it's just something minor you overlooked which is causing your issue.

Couple of simple things I would try:
1. Is the problem with both sets of wheels? I would swap them back again to make sure the problem isn't specific to a particular wheel.
2. Check your derailleur hanger to make sure it isn't bent.
3. The Park Tools videos on Youtube, suggested above, are excellent. I would follow those. If I had to guess, your shifter cable tension is either too tight or too loose, but it's pretty hard to diagnose this issue over the internet.

Also, it could be a problem with your shifter. The derailleur actually does the shifting, but the front shift mechanism determines how much the rear derailleur is moved with each click.

Thanks for the suggestions everyone, this was a big help. I pulled the hood back and the cable is all frayed and bound up at the shifter so it's not actuating the derailleur enough to hit all the gears. Looks like it's going in to be recabled.

Good! Simple solution. If your cable runs through the frame, be sure to attach a string or wire to the cable before you pull it out. That way it’ll be much easier to run the cable back through.

I had that exact same thing happen to my 105 RD a couple of months ago...I tweaked and turned everything that was within my knowledge to do, but it was stuck only reaching 3-4 cogs. I finally decided it was beyond me and took it to my LBS, and he found what you described...the cable looked like it has gone through a garbage disposal. The technician said he has seen that a lot with 105 cables. At least I know now where to look next time it happens 2 years down the road.

Yeah the mech at my LBS said Shimano road shifters shred cables. I had never heard that before but he had two other bikes currently in the shop with Shimano groups and the same issue. He said it's something about the way the cable is routed through the shifter, and it can also damage the teeth inside the shifting mechanism if you don't catch it quick enough.

When something "new" like this happens, it's often due to an "injury" - hanger or derailleur being bent or cable fraying.

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http://www.jt10000.com/

Yeah, after finding out the hard way, I got into the habit of replacing my shift cables every 5000 miles/8000 km as a preventative measure. Replacing an old (intact) cable is a breeze compared with having to perform surgery on shifters with tweezers to retreive all the little wire strands of a shredded cable. The plus side of the preventative approach is better shifting with a new cable, even if the old one hadn't shredded itself, and shifting was still "acceptable".