If you like the stock design, I would fill the butt/grip section with some kind of spray foam so you have a backing and keep the shape. Next, sand the paint and a bit (not all) of the carbon away at the crack plus a few inches on either side. Then add a few pieces of carbon over top. I would sand down roughly one layer, so the two layers of carbon you add will only increase the outer dimensions by ~1/16”.
When I’ve made my stocks, I have mainly used 2-3 layers at different locations, so you really don’t need much. I have used West Marine resin, just because it’s local to me, and I’ve gotten carbon from online composites companies and amazon. Frankly, haven’t noticed a real difference between the two.
If you don’t love the stock design, now is the perfect time to reshape it! You can make the length of pull shorter or longer, raise or lower the comb height, change the grip angle/thickness, etc. There are quite a few threads on here about building custom carbon fiber stocks. It’s pretty easy, just takes some thought and patience.