Have a look at the Squish and SquishBack commands. in THIS thread I used it to create a stair-like curve on a spiral surface, I think it serves your purpose as well.
Edit: I re-read your post, and noticed it is surfaces you want to project, Squishback only does curves, so you will have to copy-trim-paste in the same way as you did before. Have a look anyway, it also works on double-curved surfaces.
Max.