Well,as for what the bodies are, they are usually shaped and routed for you. and you can ideed get hollow ones. You can also get one-piece, two-piece and three piece bodies (you can get them with a whole lot more pieces as well).

I think it would be really expensive to do things that way, if you have access to some nice woodsand tools,maybe try it yourself, shaping and building your own body, but I promise it'll be hard work and you'll most likely mess it up atleast once or twice.

If you are happy with your guitar in general, from what you said, it sounds like your guitar just needs a good set-up and it will be back on track (however it'll still have the floyd rose).