pick an integrated from CAM for under $2000

Analytical? Should go pro way, not consumer way.
High performance, transparency in spades, speed, you’ll get it all.
Out of consumer lineup, use Yamaha AX-700U in CD Direct mode.
Hard to beat under $1000 used, in that particular regard.
Professionals use Yamaha gear for mixing/recording, why shouldn’t you?
That particular model is quite special and very well engineered (Black Gates, Elna Audio, nice yet simple linear circuit) and is very honest sounding.
Certainly not as "musical" as Marantz, Sansui, Rogue Audio, Bedini, chinese or Western tube gear, etc, can be somewhat hard and forward,
but at least it’s very precise, and lays sound bare for you to see and hear every small detail.

If you can afford going separates way, then either Phase Linear 400, Yamaha M-80 or Sansui G-8000/G-9000   https://waveadvice.com/integrated-amps-under-2000/ used as power amp only will do.
They sound quite different, of course, but have one common trait: precision/transparency.
Can use a higher end NAD/Yamaha preamp or a pro mixer with those.

P.S. Owned (many still own) and auditioned hundreds of stereos in my life, used to work as a DJ, hence the advice.