Please note up-front: I am not getting any financial reward from the following, or anything else, for that matter. All I want to do is sharing my everyday musical enjoyment.
To me - after decades of searching - there is only one answer to your question and your budgetary frame: Linkwitz LX521.4Mg (Magnesium Mid-Low). This is an entire package, not only the speaker, but includes an active ASP and 5 (!) amps per channel (10 total). All this fitting precisely into your price bracket. The Linkwitz 521.4 is the result of decades-long tinkering by the late Siegfried Linkwitz (of Linkwitz-Riley crossover fame) to create a sound transducer based on our scientific insights into the realm of psycho-acoustics, or simpler: how do we perceive music so that our brain can relax and not constantly has to recreate a musical event from imperfect acoustic clues. It is the latter demand on our brains that leads to listening fatigue. I will abstain to delve into a scientific description of why and how. Only so much: these are open-baffle dipole speakers; each speaker contains two subwoofers, one mid-woofer, one mid-high driver and two tweeters. The subs and the tweeters come in pairs, because one beams to the front and the other to the rear. That makes for 5 separate drivers (the tweeters are wired in reverse series), each of which has its own amplifier (each sub has its own, i.e. 2/channel). Moreover, the ASP (analog signal processor), takes the signal coming from the preamp (or DAC) and splits it up in such a way that each driver gets only that part of the frequency spectrum where its response curves are more-or-less flat. This leads to an overall flat and well-balanced frequency response of the speaker. You can read about this in great detail on the Linkwitz Store website or on Siegfried's own Linkwitzlab site. The speakers can be bought completely assembled, turn-key, so to speak, or as a construction set, that ships like a piece of furniture from IKEA. The price difference is a whopping $10K. I built my speakers myself. There are numerous reviews on the web about this extraordinary system, and many best-in-show opinions from visitors at AXPONA or the Munich show. Most recently, Tom Martin (of Absolute Sound fame) reviewed the system on his blog site, and called it a true "breakthrough".
I myself could not think of a more enjoyable speaker, as it does bring the music venue into my room with a realism and 3D staging that is nothing short of uncanny, and does so effortlessly without any distortions of frequency shortcomings: the bass goes deep, and remains dry and superbly focused, while as loud as the recording demands. Well, two subs, each driven with 250 A, leave nothing on the table. I listen to every musical genre (except Grunge), and I have never felt that there should be more. I get great performances from intimate jazz lounge recordings and solo singers or instruments as well as from large-stage synthesizer-heavy stuff such as Dead Can Dance or the recent Blade Runner tracks, which are just mind-blowing.
I could get on and on, but I think you get my drift: for your budget there is simply nothing else out there coming even close to what the LX521 system offers.
A final note: the Linkwitz store is direct-sale, no middle men, no mark-ups, no ad costs in magazines (besides a very small one in the recent Stereophile pages); however, if you are interested, many happy users such as myself have agreed to join the international network of Linkwitz Lounges, where we open our homes to perfect strangers and have them listening to our set-up, before they spend beaucoup-bucks on something which turns out to be a compromise. My lounge is located in our living room, meaning: a realistic setting, such as your own. There are no wall treatments or any other fancy stuff obfuscating the fact that a demo system could be far from perfect in your own setting. So, if you are serious and not too far from Silicon Valley, please shoot me a message and we go from there!