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

The Emotiva ERC-4 has XLR/Balanced outputs.

In your budget and a really nice machine too!

(Actually all of the Emotiva ERC models have XLR.  The ERC-3 is excellent also)

I have a 352 also and went with Advance Paris X-CD9. New is outside your budget, but you might find one used that fits. There is also the CD7 model but no tubes on that model..

Used Teac might fit your needs.

I have a Rotel RCD 1572 MKII with balanced XLR outputs.  It sounds great.  It’s been around for a few years so should available on the used market.  

Sony xa5400es has XLR, RCA, HDMI, Digital Out, sounds terrific

seller says verify still available

https://www.highperformancestereo.com/digital/sony-scd-xa5400es.html

another, from Japan, verify menu language and voltage

https://www.ebay.com/itm/197693283813?_trkparms=itmf%3D1%26aid%3D1110006%26rkt%3D4%26mech%3D1%26algv%3DSimVIDwebV4WithCtxRankerV1UnifiedFeatures%26pmt%3D1%26amclksrc%3DITM%26sd%3D326924970281%26sid%3DAQAKAAAAENzuT17fCLamfCG%2FHYihff8%3D%26itm%3D197693283813%26noa%3D0%26plcampt%3D0%3A58289169012%26algo%3DHOMESPLICE.SIM%26brand%3DSony%26asc%3D20231107084023%26ao%3D1%26rk%3D4%26pid%3D101875%26b%3D1%26mehot%3Dnone%26lsid%3D0%26meid%3De8c86cec7ebc4548b276122671edc91b%26pg%3D2332490&_trksid=p2332490.c101875.m1851&itmprp=cksum%3A197693283813e8c86cec7ebc4548b276122671edc91b%7Cenc%3AAQAKAAABELbQdNnV9E6H66rV4nIZYAZCOANuR76zl8wG%252FmKawEdd%252FZzO2T5yUdpwsFRr7Sz0JOb03uk3zP%252F5c0qH4DjenjeJt%252BVGJEzqp%252B4wVzm85OzBhx56P%252Bm7kZBbqlC1%252BvMFfP5AEQNFXRh6XwGfGLmitR0svYHwn6i8SumZpt2L8dlVEpyNMZ9UkFxypiVLv6vLYHUMUBqX38LcNv7bVJ6OWPJD8Iu7qnAUlYf6fwtp2RZpOTczowwDuqr1xhO7T2%252FvokvikLIw4FSC3xEso2nF5vwMgDg0fIYsendmYP9%252B%252BeOYMjrlArbAEYNC%252BZVMsVx1uTmTBZCnroVSIDWFyJXVoVg4pc%252FdRV7ARWq%252F3D1cvX%252BQ%7Campid%3APL_CLK%7Cclp%3A2332490

It plays SACDs also, and sends DSD out, not auto conversion to PCM as some units do

I asked for advice here, found one with low hours on the laser

https://forum.audiogon.com/discussions/sony-sacd-player-scd-xa5400es-yay-or-nay?highlight=sony%2Bxa5400%2Byay%2Bor%2Bnay

https://forum.audiogon.com/discussions/sacd-players-models-with-dsd-processor-used-and-new-not-dsd-conver?highlight=sacd%2Bdsd%2Bpcm