Help me find my ideal Stereo Integrated Amp

1:  Audition the Devialet Expert 220 Pro listing at $10k.  It has all you’re looking for in a sleek Class D design.   
2:  Better IMHO is a preowned Mola Mola Kula.  It should come in may be at or a little above your budget.  It will be hard to find but not impossible if you are patient.  
3:  +1 on the Bel Canto E1X, another sleek Class D design.  

All will have different SQ characteristics.  All have more than adequate power to drive almost any speaker.  Audition a must.  Good luck.  

Gato very good service also and European quality.

NAD M33, as mentioned. Class D with Eigentakt Purifi design.

McIntosh MA8950. You will need a streamer.Class AB.

If you concentrate on the quality of sound and performance of the integrated amp, you might have to consider using a stand alone DAC and streamer as opposed to a do it all receiver.

Luxman and Accuphase make superb integrated amps.