Hoenstly,
I don't think it exists. You could spend double that and have a short list of candidates. Used will get you a lot closer to your goal.
If you talk to the folks who make 'em most will readily admit that to engineer to that price point, they must make some compromises. The choice of which compromises to make, and the execution is why there are so many speaker lines and so many different design theories.
By stating that you don't want monitors, sounds like good bass performance is near the top of your list of priorities. If so, I think the floorstanders will give you some tradeoffs in the other areas mentioned. If you find the killer $2500 speaker that does it all, please share!
Spencer