I agree with @Dincrest that ESP makes a lot of sense and the LTD stuff is very good for the money. The used market is the way if you want something atypical, since you're much less likely to find unusual designs across all price ranges. I might also consider Reverend basses. Probably also used territory to get a fair price, but people on here love them.
While I love J basses, you're right that there's A LOT of what people call on here "Fender-shaped objects" (FSOs). It takes a little hunting to find alternatives, but they're out there. In general the big companies are conservative with what they release, so you find more classics than oddballs at affordable prices. It's a bit of a shame, I'd love a Rickenbacker 4000 at a lower price, but it is what it is.
In terms of finding a tone you love, look to bassists with tones you like. Then in the shop leave the EQ close to flat or give gentle bumps. This is a generalization, but usually basses don't sound great with the amp EQ boosted way up: it either gets muddy or abrasive. So if the bass isn't for you with a more or less flat EQ, then find another bass.
While I love J basses, you're right that there's A LOT of what people call on here "Fender-shaped objects" (FSOs). It takes a little hunting to find alternatives, but they're out there. In general the big companies are conservative with what they release, so you find more classics than oddballs at affordable prices. It's a bit of a shame, I'd love a Rickenbacker 4000 at a lower price, but it is what it is.
In terms of finding a tone you love, look to bassists with tones you like. Then in the shop leave the EQ close to flat or give gentle bumps. This is a generalization, but usually basses don't sound great with the amp EQ boosted way up: it either gets muddy or abrasive. So if the bass isn't for you with a more or less flat EQ, then find another bass.
