There are a few ways to go about doing this, but all will require some time with sand paper.
1) You could sand the whole thing down starting with a rough grit and going finer as you get closer to the actual carbon fiber
2) Use something like Carbolift (http://www.carbolift.com/
" onclick="window.open(this.href);return false;) to get a lot of the paint off then finish the rest off with fine sandpaper. DO NOT use normal paint stripper, the chemicals in those things will eat away at the epoxy.
3) I would definitely recommend clear coating the bike. A lot of bikes that have that raw look have a matte clear coat. I would make sure that the clearcoat is also UV protective as significant exposure to UV can eventually degrade the epoxy in the carbon fiber.
In any case, sounds like it'll be a fun project (albeit a bit tedious at times....)!