6000 dollars CD player

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/

No... no... no...

Don’t waste your money on any CD Player - none of which provide the sound quality of one of the better R2R DAC’s with a good CD transport.

There is no CD player that comes close to the sound quality of the good R2R DAC’s - none of which will cost you more than about $2500, if that.

Here’s a thread, which identifies the best / better ones (though, the Schitt Yggdrasil Analog 2 compares quite favorably to most of these in this thread).

https://forum.audiogon.com/discussions/some-dacs-i-am-considering-any-thoughts

And... you can always start ripping your CD's to FLAC files on a good server (Bryston BDP 3, etc.) to make access to your music a very convenient exeperience!

Pick a Mark Levinson- new or older--great-=-