Can anyone recommend a smooth, rich CD player?

One of the smoothest richest sounding cd players was the venerable pioneer pd-65. Many now use it soley as a transport but it had a very smooth dac. If your system is treble bright or you want a rich sound this may be one of the best and cheapest ways to achieve your goals.

I would listen to the Cary 303/300. Listen to the tube output. It is special.

I second Entrope above with regard to introducing a tube if you want to veer towards a richer sound. Re the 508.24, I owned one and a/b'd it against a Granite 657 tube player. I and all who heard the comparison preferred the Granite. It wasn't even close (which surprised me because I'd heard such good things about the Merdian). The Meridian sounded thin--clear, but cool and analytical (too much so)--compared to the Granite. The Granite's tube output likely was part of the reason. The Granite's more $$ than your budget, but I'd check into the recommendations above that have a tube output. Surely you'll find one that sounds rich without sacrificing detail.

I will second the Granite 657 CDP. I replaced a very well respected unit with the Granite and am quite pleased with the outcome ! It just has 'more' of everything that I enjoyed with the old one .
If you can, wait and save up for the Granite, it won't disappoint you. They also offer an in home demo period with a money back guarantee .
Good luck !