Wow, seems like you want your cake and eat it too.
You really can't get very far picking speakers based on the opinions of others.
Wholeness I transcribe as coherency, the seamless integration of all the drivers. In general the fewer the drivers the better.
Deep soundstage is largely a factor of how much open space you have between/behind the speakers, but by this I infer that you mean 'not forward/in your face' presentation.
Neutral, yet slightly warm? Pick your medicine.
Very revealing yet forgiving? Again pick your poison.
'Lots of punch (nothing muddled about it)' to me means good/clean dynamic response.
'Cleaniness' can mean accurate, detailed, and/or correctly rendered tone.
'Sound airy without being lean' to me says extended treble response without thin midrange.
Being engulfed by the sound from 10 feet away should be easily attainable. A balanced performance at lower sound pressure levels (spl) in my experience translates to higher than average efficiency, say starting around 92 dB/w/m and having a (gasp) loudness control.
For A/V and music use you want highly dynamic speakers that can handle high spls. For better quality bass performance throughout the room recommend multiple subs (up to 4).
I'm a fan of active speakers, so here goes...
Active mid-field studio monitors should fit your bill quite well (dynamic, coherent, good imaging, balanced tone). Quality monitors (in/below your price range) would be well into the neutral/revealing end of the spectrum (you'll have to decide if you want to hear the actual recording or not). These are the very speakers used to make the recordings you listen to, so what could be better? My choice for you is the JBL 708, well within your budget (spend leftover on more/smaller subs). They can be 'in your face' and the soundstage width a bit constrained, but adjusting toe-in solves that. The 708 is just a black box to look at but very well respected and comes from a company that has been in the whole business (designing and building drivers/crossovers/amps, testing facilities, for home and professional use for 70 years). See my recent review for more information.