More food for thought:
Why go for an Epiphone? There are other LP copies out there, cheaper, maybe lighter wood. Plenty of decent-quality guitars, most, if not all of which are built in the same factory as the Ephiphones.
You'll be less reluctant to experiment, that's for sure.
Instead of thinning out an LP you can look around for a Melody Maker --they go cheap, they're great guitars, extremely lightweight, easy to adapt for LP humbuckers and they're Gibson
Otherwise, just chamber the LP from the back, take out as much wood as you need, then cover it again --I'm using the back of an old acoustic for that--who ever looks at the back of a guitar?