Re: To make a Strat sound more like a Les Paul...
If you were building one with all new parts from say Warmoth or USACG, I'd say mahogany body with maple top (granted, lam tops are typically 1/8-1/4" thick... arched tops vary from 1/4" to 5/8" in the same piece of wood because of the varying thickness). Go with a 24.75" conversion mahogany bolt on neck with rosewood board. Rout for a pair of humbuckers and a tune-o-matic bridge, and I think you'll be in the right neighborhood. It won't be perfect, but it'll get you as close to an LP as possible with a strat body.
I can only see someone doing this if they hated the LP body shape, because the strat I outlined above would likely be just as heavy as a real deal LP. Maybe it's a comfort issue.