I want something completely different than the Super Strat sound...more of a Les Paul, fat/thick...freight train sound.
I love RG's honestly because to me they're in the middle between the twangy ash or alder Strat and the beefy warmth of the Les Paul. Coupled with the HSH configuration they're IMO the most versatile guitar I've played.
That said I've found myself at times wanting a bit of that late 70's / early 80's rock warmth that to me comes best from an LP. The LP is one of the best instruments made. I just don't like how it feels, how it looks, or how the controls are laid out. I love the neck. I'm not too keen on the string spacing, 22 frets, or the 24.75" scale but I can live with those things.
Here's some ideas.
Get a Destroyer or an Iceman. A set neck would probably be best. Something with a fairly big mahogany body.
Get an old RGT. Also a mahogany body. Get a fixed bridge or block one of the trem models.
Get an RG421 or something, also, with a mahogany body.
Put Dimarzio Super Distortions or PAF 36th Anniversaries in or Seymour Duncan Whole Lotta Humbuckers in any of the above.
OR.... get an FRM150.
All the same, none of these things are the same sound-wise or aesthetically to a Jem. I agree with the others that without a monkey grip it's not completely a Jem but more of an RG.
You could also find a mahogany body from Pearle, as you mentioned, or try and find a JEM7EAFX which looks like a cool guitar aside from that hideous "VAI" graphic on it.