I decided to pay a buddy some chump change to do this for me as time is not my friend and low and behold its a direct swap as far as the case is concerned. I'm not 100% sure about swapping individual gears but it sure looks possible. It's still gonna be a minute before I drive my car but as far as the question if fitting an 03-05 Civic Hybrid gear set into an 07-08 gear box OR you can use the HCH trans and buy a Fit clutch side trans case, 100% yes.
While I never have personally taken apart a trans before I wouldn't hesitate to do it myself next time (I watched). It took him 2 hours and he said it was easier that K series for reference.