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

CA CXC v2 transporter fits your bill.  This one is open box but still carry 3 year warranty.

https://www.safeandsoundhq.com/products/mcambridge-audio-cxc-v2-dedicated-cd-transport-open-box?variant=52324136780143&country=US&currency=USD&utm_medium=product_sync&utm_source=google&utm_content=sag_organic&utm_campaign=sag_organic

The DAC inside a new CD player in a similar price range is usually entry-level at best. That’s why you’d want to enhance sound quality with an external DAC. The sky is the limit, but there are many high-quality sub-$1k DACs that can deliver convincing 3D soundstage performance when paired with a good transport. The Harmony Micro DAC is one example, and the Topping D90 III Discrete is another. I’ve owned both, and once you go down this route, you’ll likely receive many more recommendations.

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?