Looking for a CD Player w/XLR Outputs...

As @lanx0003 is implying, you have an $8K integrated amp.  A $600 CD player, let alone one with XLR out (presumably at the expense of something else), is a mismatch for such a nice hifi centerpiece.  Depending upon your speakers (and interconnects and room acoustics), doubling your budget from $600 to $1200 will probably yield very noticeable improvement in sound quality.  For example, go ahead and get a $400 CD player or transport.  But then also get a $800 DAC - even a used model that is 1-2 years old will be quite satisfying versus whatever you’d find in a $600 CD player.

Agree that at your price point the quality of the cd player will be well below what your amp can do...Schiit, SMSL, Fosi all make low cost DAC's with XLR out...the Cambridge CXC v1 is identical to the v2 except for cosmetics...if the CD is for convenience or background only, just get a pair of XLR-RCA adapters for the CD player...

The McIntosh MCD85 SACD / CD is the prefect add to your MA352 but $600 would only cover the tax. Maybe there’s some gently used SACD options in the marketplace. I mention SACD since that’s where your best chance of getting XLR ouputs.

MCD85

Please note a decent set of XLR cables alone will also easily cost $600 for a very short distance.  

Albeit a much older unit, I wonder if the MVP 861 would suffice?

Oppo 95 or maybe 105 would be in your range.