Thanks for all the input, folks!
I think I'll probably settle on a used Schecter Solo-II Custom if I can find one at the right price, and it isn't prohibitively heavy. Seems like that's the best features/quality/price combination that'll have those LP-esque attributes, and I find the headstock and body shape to be among the most-attractive implementations of the Les Paul style. Some of them just look fat or clumsy to me, but the proportions of the Schecter seem a little nicer to me than those of Gibson and Epiphone...it is, I grant, a subtle difference.
If I'd found something like a carved-top Tele body with the 24.75" scale length, stop tailpiece, and correct pickups, that could also have done well. But that combination seems rarer.
