CD player

I would recommend concentrating on improving your streaming (Streamer and DAC). My streaming is as good as my CD, stored files, and analog. This is possible at many price points. A CD player is a combined transport, streamer, and DAC. If you put your money into a good streamer and DAC. Schiit makes some great DACs: Gungnir and Yggdrasil. A good streamer and you should be able to listen to a nearly infinite library (including the music you own on CDs) for almost no cost.

I have 2,000 CDs that I never listen to because I can listen to them without getting up out of my chair and often they are at higher resolution… although I seldom do because I have found so much new music to listen to.

The Cambridge AXC35 at only 350 bucks would be a great match to your ML 35XTI folded tweeter. A really nice sounding unit. 

I wanted to get a cd playing system that I thought would be good enough that I wouldn’t be upgrading from it for a while so got an Audiolab cdt 6000 and a Denafrips ares II, I’m very pleased with it. After buying the pieces, reading reviews and others' comments about them, and my own listening I think I made a good decision and am pleased with it, not looking to upgrade. My only recent comparisons are an NAD cd player that I thought was bright and fatiguing and a Schiit modi 3+ that was quite good- no sins of comission just omission, you loose some detail but the overall sound was pleasant.

Just another option,  I had over 1,000 CDs and used a Bluesound to burn them into digital files and used it to “stream” my CD library. I would never go back to playing CDs, so I agree with ghdpentice for the most part. Using the Bluesound software is so much better then a CD player. So this way I didn’t lose my great CD collection. I have now moved up to a Aurender which also has a great streamer built in. So you get to play and manage all your CDs as easy as streaming and still get a better streamer. Some Aurenders even have great DACs built in or you can get one without a DAC. You can bypass the Bluesound DAC. 
Sorry for giving you yet another solution, but it worked out very well for me to not upgrade to a better CD player (I had a Rotel by the way which was a great sounding player).