Best CD player under $2000

For me the best is:

EternalArts Digital Player DP DAC MkII

For my ears I've been really impressed by the Musical Fidelity M3scd. When A/B'd against a Bluesound Node 2i playing an MQA stream (which I also think is excellent for the money) I found the MF presents a wider soundstage with a comfortable balance and control of the sound. 

+1 on separate transport. I recently approached just this question and got a Cambridge CXC and an MHDT Orchid DAC. The CXC is solid (there are other solid transports, of course) and my DAC is great.
I may be repeating things you've read, but here is my bullet list for the separates route:

• CD's are yielding to streaming. I already find myself using my streamer way more than my CD player.
• Good DAC can accept multiple inputs — I run both CXC and Node 2i streamer through DAC. Thus, improving sound of either digital source (and a third if I connect my laptop) could be done with one switch of DAC.
• If you get a tube DAC you can tube roll. Cannot do that with most CD players.
• A CD transport has no money spent on an internal DAC; it does one thing well (if it does it at all)

Do yourself a favor: convert your CDs to flac!  I've done my 900 CDs a while back and now, i have all my collection at my fingertip!
CDs are know to degrade with time.  So ripping them fix that degradation problem.

On Windows, use EAC (Exact Audio Copy), on Linux abcde.
On my case, i play my music with free Volumio on a Raspberry Pi 3 hooked to my DAC via USB (async).

I second Electrocompanient