6000 dollars CD player

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-=-

What you're listening to in a CD player is the DAC, not the transport.   The CD reader is just what you get from a $20 CDROM drive.   Really.

It's the DAC you're listening to.

I run a Tascam CD player because it's a piece of pro gear, and being pro, is more durable and reliable than consumer stuff.  I run an optical line from it to my DAC.  The sonics from the CD player are identical to the same track being played back from my laptop digital files.

But if you've really got $6k burning a hole in your pocket, then you're the kind of guy this industry loves.