Suggestions for CD player $2-3k used?

If you are looking to run your player balanced, I would think about going with the Ayre. The products that they produce sound much better when run with balanced cables since they put their money into designing fully balanced circuitry. If you are going to run single ended, I would audition the Modwright Platinum Truth Sony 999ES or the newer versions that Dan mods.

A Modwright Sony (get a copper umbilical from Dan if you buy a used one with the Revelation Audio Silver umbilical) would seem to meet your needs the best other than being single ended. Best value by far.
The Meridians and Sim Audios I've heard (don't remember which ones other than the Moon) have tended to be cool and analytical. Didn't care for the Cary 303-300 either: thought the Muscial Fidelity A5 was better.
Liked the Ayre CX7e and, as I only heard it in single ended mode, it could be very good indeed. Didn't find it uptilted.
As suggested above, an AR CD3 could be a very good choice also. I have yet to hear one but the reviews seem to match your criteria.
Good luck.

Hello Mitch- The CCa's I referred to are 10K hr tubes. They should out live the love affair I have with the VK-D5 and it's musicality. By the way- If you should pursue these excellent(and highly accurate)tubes: be certain to find the 60's(dark grey getter support), and not the 70's versions. The later tubes were terrible on top(pumped razor blades). I really don't want to be restricted to one tube selection either(as the SE/6H30 version is). The D5SE also provides less voltage at the outputs than the D5(about half). A serious consideration for me, as my Tact 2.2X doesn't provide much gain at it's outputs. For some of the CDs I own(recorded at lower levels)that can be a drawback to my listening pleasure(I like realistic DB levels). A used VK-D5 at about $1500.00 and six NOS CCa's at about $700.00 would fit your stated price goal nicely. You might have a harder time finding someone that wants to sell their BAT, than to find the tubes. Oh- with regards to bass response: My system is flat to 20hz through the VK-D5 player(Stereophile Test CD #2 for test signal). I forgot to mention that earlier. Bluebook CD repsonses are truncated at 20 and 20kHz of course. With the TacT's pink noise generator, I measure 3db down at 14hz. Like I said: the VK-D5 delivers the music. If you get one, and something's missing: It's either not on the CD, or the system/cables/interconnects are holding it back. The VK-D5 and Kimber Select 1130s are a match made in heaven, BTW.

If you care to research the CCa further:(https://www.tubeworld.com/6922.htm) has some good info at the bottom of the page. Further info on VK-D5 per Stereophile review:(http://www.stereophile.com/digitalsourcereviews/570/) I noticed that a couple of TAS writers/reviewers had VK-D5s in their reference systems until just last year. The TAS review belabored the point of the VK-D5SE's alledged, "dark" voicing, to the consternation of a number of BAT lovers. There were some humorous 'letters to the editor' in response.

Mitch2: No, I have not compared the CD-3 to the CD-3 Mk. II. The latter costs roughly 10% more than the former, and as audio occupies the same universe as everything else and you thus tend to get what you pay for, it surely must be better. And as your Aerials are very fine speakers, I would think that you would benefit from the Mk. II.