What is the most analog sounding CD player under $

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.