Greetings Radioman,
It sounds to me like you and I have similar taste. Let me make a few observations, and then a few specific suggestions.
To sound good at low volume, a speaker must be very articulate and have very good dynamic contrast - otherwise, you keep wanting to turn the volume up. So you want good quality drivers and a minimum of boxy resonances which can blur the notes and smear their decay, which reduces both the articulation and dynamic contrast of the system. Also, to sound good at low volumes, a speaker should be voiced a wee bit on the warm side, since at low volumes the ear has a harder time hearing the bass. This characteristic of human hearing also puts a premium on smooth midrange performance for low-level listening, since at higher volume levels the bass can subjectively mask midrange peaks and resonances.
If you're going to listen at medium-high volumes, you want a speaker that is relaxing, non-fatiguing and free from dyamic compression. Again, you need high quality drivers, a lack of boxy artifacts, and smooth, even voicing. Harshness in the upper midrange and lower treble region is especially annoying as the volume level goes up, because this is where the ear is most sensitive.
A significant but almost universally overlooked factor in creating a non-fatiguing experience is the speaker's radiation pattern. Briefly, you want the reverberant field to have the same tonal balance as the first-arrival sound. Where there is a significant discrepancy, the eventual result is listening fatigue (headache) as the ear/brain system works to integrate the two dissimilar events. Where the two sound the same, which is the case with live music, you can listen for hours and hours (assuming the speakers otherwise sound good). You may have noticed that some speakers sound great for the first twenty minutes or so, and then you're ready for a break. Often the culprit is the discrepancy between the first-arrival and reverberant sounds.
Uniform dispersion with respect to frequency is rare in a loudspeaker because of driver beaming. In $2k-$3k price range, most speakers are two-ways with a roughly 6.5" woofer and 1" dome tweeter. The radiation pattern is omnidirectional in the bass, then narrows gradually until the woofer is starting to beam at the crossover point. The radiation pattern blooms again as we go to the tweeter, then once again narrows as the tweeter starts to beam. There is no way to equalize this speaker for smooth reverberant field response.
There are two approaches that do a good job of getting the reverberant field to closely approximate the same tonal balance as the direct sound, and both start with the woofer. Most speakers have omnidirectional radiation in the bass, so the wider the speaker's radiation pattern throughout the rest of the frequency range, the less discrepancy between the first arrival and reverberant sound. A few speakers have dipole woofer systems, which produce a figure-8 radiation pattern, and a good designer can then tailor the midrange and high frequency radiation patterns to blend well with the bass. Unfortunately, most dipole speakers are out of your price range.
Speakers that I think do better than most at meeting these criteria include:
1. Shahinian Obelisk. Very spacious sound, warm voicing, deep bass. The presentation is more like what you hear in a large concert hall.
2. The Cliffhanger Bulldog. Very low cabinet coloration, lively voicing and very good articulation. The presentation is more like what you hear in a small jazz club.
3. The Heil Aulos. Warm voicing with good soundstaging and timbre over a wide listening area.
4. Maggie 1.6. Utterly boxless sound, but not as well suited to low volume listening. Suffers from some dynamic compression, but generally very easy to enjoy long-term.
5. Heil Kithara. A bit outside your price range, but deeper bass and richer presentation than the Aulos.
6. Gradient Revolution. A bit more outside your price range, but smooth and boxless all the way down into the bass and very relaxing long-term.
Disclaimer - I'm a dealer for Gradient and Cliffhanger.
As you audition, here are three quick tests you might find useful: First, listen at extremely low volume. Is it enjoyable? This will make any midrange peaks stand out. Second, listen at a more or less normal volume, but only a few feet from the speakers, and on the tweeter's axis. This will isolate the direct, first-arrival sound from the reverberant field's contribution. Finally, turn the volume up louder than normal and go into the next room, leaving the door open. From here, all you can possibly hear is the reverberant field, and you want it to sound convincingly like live music. If the speaker passes all three of these tests, put it on your shortlist.
Best of luck in your quest!