What is the most analog sounding CD player under $

I found it! In an antique shop covered with rust and gunk.  The transport had to be prodded with an ice pick to get the tray to open.  The CDs skip, distort, and the music can barely be heard underneath the cacophony of debris.  Just like vinyl!

If you want 'analog' sound from digital---get isolation for your digital and preamp. Simple eh? (Canadian eh). Otherwise it does not exist. Seriously.

What do you mean by isolation - physically or electrically? To the OP, I'm also in the same situation as you and have decided to look for a better DAC than a "better" CDP. I think that approach provides a better longer term path for future growth.