6000 dollars CD player

All you need is an Audiolab CDT 6000.
The best transport without a DAC no matter the price. Only $549.00

Bryston BCD-3. No need to spend $6,000!

If you are committed to getting a CDP look Brands and Models that have a VRDS
(Very Rigid Disc Clamping System) Transport and Sony KSS Laser.

VRDS was developed by TEAC and is used by the worlds finest CD players like Wadia, Krell, Spectral, DCS, Esoteric, Tascam, and TEAC.
Top of line: full metal,
Middle one: metal-carbon composite hybrid
Cheap one : full plastic.

I would say that Esoteric is your best bet for your budget
Check out - just above your budget
https://www.audiogon.com/listings/lisa7ib2-esoteric-k01-cd-sacd-player-dac-cd-sacd-players

NEO was the best VRDS ever produced 
https://www.esoteric.jp/en/technology/vrds_neo

DCS Vivaldi One
https://www.dcsltd.co.uk/products/vivaldi-one/
http://www.theaudiobeat.com/highend2017/highend2017_dcs.htm

Good luck

Why not look for a used Esoteric SACD player.  I use a K-05 and love it.  I don't have many SACDs, but it plays regular CDs fantastically!  You will be happy with the fit and finish, I promise.  

Else, I would just go with a Marantz transport or something like that to a good DAC like others have suggested.  I like the PS Audio DirectStream DAC, which you can find used for around $3500.

If Classical is your aim, there is no CD player I would take, at any price, over the Ensemble Dirondo. I heard it at Munich and it really made magic. 
http://ensembleexperience.com/dirondo-drive/