.....the tonal difference is because the SG's and Les Paul types are Mahogany bodied and (some) have Mahogany necks whereas mostly light tone woods like alder, poplar, and stuff don't bring that "full" sounding Gibson sound.
But keep an eye out for pedal-type processors like the Digitech RP-100 and the like. They might be your alternative also.
But this RP is a bit noisy with single coil pickups though.