I hadn’t noticed the marks on the chainstay, but I wouldn’t be terribly concerned about those–they look pretty much superficial. Do they pass the coin test or are there any indications that they are anything more serious than just paint chips?
As for repairing the seatstay, here’s what I’d say: with consideration given to your resources and ability level for doing paint/cosmetic work you need to decide what you’ll be happy with as a cosmetic outcome. Would you be satisfied with having a section with visible carbon fiber? Would you be happy with potentially non-matching white paint? This is what separates Calfee and Kane–you’ll end up getting your bike back in a condition that “resembles” new. Some come back looking perfect, some come back different than new but still cosmetically good (i.e paint may be different color, may be missing logos/stickers/emblems, it all depends on the location/extent of the repair, the complexity of the designs on your bike, etc.
The number one thing to consider is that while this is not a particularly technically challenging process, it will require a lot of time and attention to detail. If your time is really valuable or you have better things to do then you should just bite the bullet and send your bike to Kane or Calfee.
Once you’ve decided to do it yourself, you’ll need to buy materials. Depending on the quantities that you buy you’ll either end up with more than what you need of everything or a lot more than what you need of everything. You’ll just have materials left over for future projects…hopefully fun stuff and not frame repairs. You’ll come out ahead on cost even buying 10 times what you need for this project.
I’d recommend US composites and Fibreglast. There’s some stuff that you will need that you can really only find or buy economically from one or the other. You’ll need carbon fabric (plain weave, 5.7 oz/sq yd is what I’d recommend–twill weave will be harder to wrap/drape–US composites clearance materials will be cheapest, unless you buy sample-size swatches from Fibreglast). You’ll also need peel-ply, and bleeder sheet. Both can be bought from US Composites vacuum bagging materials section. You’ll need epoxy (I’d recommend the US Composites 635 epoxy system with Medium hardener). You’ll need cutting tools (a sharp razor blade will work if you have some kind of anti-fray product such as edge tape or an anti-fray drip, otherwise you’re best using an Olfa craft-type cutting mat and roller type cutting blade). For compression you’ll need either 20% shrink tape or just good old fashioned electrical tape wrapped tightly. You’ll need high-temp tape to secure the shrink tape, since the shrink tape is activated with heat. Vacuum bagging is always an option as well, though it is much more challenging to seal a tube that small compared with using a wrapping method for compression. Vacuum pumps are expensive, and the only way to do it any cheaper would be to use a venturi (which still requires that you own an air compressor with a suitable flow rate).
You’ll need mixing cups, stirrers, brushes, squeegees, painter’s tape, lots of plastic drop cloth to cover up your work area, other parts of the frame, etc. You’ll also need a range of sandpaper: 120, 320, 600, 1000, 1500.
I think I spent $180-$200 on materials buying the smallest or second smallest quantity of everything, but I have enough of every consumable good to do probably 10 more projects of the same size.
If this still sounds like something you’re up for, start buying and start researching vacuum bagging composites–95% of the underlying principles will apply, you’ll just likely be using a simpler method to apply compression. I bought a whole roll of shrink tape and probably ended up using 5m of it when I repaired my top tube. I’d be happy to send some your way so that you can save on costs.