Les Paul Studio in ebony that doesn't break the bank.

Maybe itâ€s the lack of binding

Could be. But if you hook that sucker ( Or a Fender Prodigy) Up to an Orange CR120 (Because the OR120 makes me cry) with the right pedals, You'll have one of the chunkiest tones I've heard in awhile. I think you can get the same effect with a Gibson Explorer however.