CD player suggestions...

@peterpetre 

No. But an interesting idea. Do you know whether they come with appropriate IECs? I may be getting a Project to compare, first

Cambridge Audio CXU is strong contender in your price range, if you can find one. Plays lots of disc types including SACD, equipped with digital outputs in case you want to use it with outboard DAC and pure audio mode which disables all circuits other than audio path circuit for better SQ. 

Putting a $600 Audiolab CDT-6000 through a $2500 DAC is 5X the specified budget. Go with the Marantz CD-6007. Not often noted, Marantz has two digital filter options, something not often seen outside separate DACs. It is the first CD player I've owned that sounds noticeably better than the others.

Do you have a good DAC? If not, buy this first. All $800 CD players are going to have a very weak DAC.

Soley out of curiosity, I own one of the Emotiva CD3 players and unfortunately have little good to say about it. If I could, I would like to try yet another DAC with it, specifically the AudioQuest Dragon Red. Being as the AQ only allows for USB connection, is there an adapter to 'fix' this? 

 I mention it here because mechanically the Emotiva is good, but the rest of it, not so much. The OP could do something like this, maybe?