Hey Drew,
Good advice here from others. And I always say that Alembic can build whatever you can dream up so I hope it comes together for you.
But I'll add that the criteria you've stated strikes me as bit funny. "6-strings" I understand if that's your thing. But your only other concern is the weight? No mention of which model, electronics package, body shape. You're even willing to go short-scale to save weight. It's like saying you're interested in an all-wheel-drive car that's blue.
The overall weight of an instrument likely has an effect on its sound. (So does the scale-length in my opinion.) I would guess sustain is directly affected by how "vibration absorbent" an instrument is. But I'm really only guessing. Mica at Alembic is the one you need to talk to. She can describe what different wood combinations do to the tone, and the weight.
Hey, a 4-string would be lighter.
I don't mean to bust you - tell us more about what other details you're interested in.
Cheers,
Jimmy J