In that price range, have you considered Dean basses? They have some super-strat-ish shapes, but they also make that Dimebag signature shape (in various flavors from pointy to rounded).
You may also look at Epiphone - I'm pretty sure that Explorer basses are a thing. (A flying V bass might be too metal for your tastes, maybe.) Dean also makes these shapes.
Warwick might also be a good option - something like the Warwick Corvette - albeit more traditional (but not a P or J copy) and possibly pricey.
You may also consider BC Rich - they make more unique body styles, like the Mockingbird, but they will also likely be outside of your price range.
Hope this helps. Guitars tend to have flashier designs (and sometimes amplifiers) due to guitar culture, rock and roll, etc - electric guitars are seen as much as ghey are heard, and so the image is part of the market for instruments and geat. Bassists and basses simply aren't as popular (outside of bassist circles), and so thr market tends to skew more to the conservative side. We're pretty boring!
It is what it is.
