Re: Anything sound like a Les Paul but feel like a Fender?
I feel the same way about SGs- something about the geometry just doesn't suit my hands or my body.
+1 on a PRS McCarty- the slight extra thickness of their body really does bring 'em a step closer to Les Paul territory. And they hang naturally on you like a Strat. To me, though, PRSs feel closer to Gibsons than they do to Fenders. It's the scale length (closer to Gibson) and the set necks.
In terms of 25½" bolt-on axes, pickups make a lot of difference. Someone recommended me a DiMarzio The Breed for bridge position on a tremolo Strelecaster that sounded a bit thin, and the Breed has made it pretty fat sounding. It definitely has as much girth as some of my Gibsons, though not their warmth. And it feels 100% Fender under the fingers.
I have other 25½" axes with bridge humbuckers: a PATB-3, a JB, a Pearly Gates Plus, a Fender Atomic, an 80s Schaller and a 70s Gibson T-Top. They each sound good in their own way. But I'd say that Strelecaster is closer to the tone of a Les Paul than the others.