Can anyone recommend a smooth, rich CD player?

My choices would be Meridian 508.24 or Audio Research CD2. Both will be what you're looking for but ARC will have better bass. Neither is bright or hyper-detailed. Both are very smooth. Ways better than your CD33 and will not sound bright on less than perfect recordings. My personal preference would be towards the ARC. But in any case these 2 players are the real deal.

AA Prima, Cary, CJ, Copland

Another vote for the Meridian 508.24. A great cd player, especially at it's used price point. It's essentially a neutral player just on the warm side of neutral--very smooth with good low level detail retreival. It also has one of the lowest jitter ratings that Stereophile ever measured. 146 pico seconds, if I remember correctly.

I've been trying to sort this out for the past 3 years...

In my opinion (and experience) the Cary players will only sound warm if used in conjunction with tubes somewhere else in the signal path. If you go the Rega route you'll get great warm and musical mids but at the cost of rounded out highs and lows... Ideal solution based on equipment that I've heard: Electrocampaniet with solid state gear, or Cary with a tube pre...

You may also want to consider the Audiomeca Keops. It is based on a highly modified CEC belt drive transport, and has the attributes you are looking for.