Advice on buying good CD player that will outperform my Primare cd31

Try Audionet ART G3  .

It still boggles my mind that people are willing to drop this amount of dough on a cd/transport in this day and age...
and if you simply must have one then try  this one for a fraction of the cost, and use the rest of the money for a DAC.

Cambridgeaudio CXC

https://www.cambridgeaudio.com/en/products/cx/cxc

I would recommend Onkyo C-N7050, it has a foot in both camps, being both a CD player and music streamer. A truly versatile bit of kit.

I am solidly in the "transport + DAC" camp these days.  The DAC in the Primare should be wonderful, so it may be you just don't like the flavor of the R2R DAC in the unit.  I would try out different DACs before I spent too much money on an all-in-one CD player.

The Marantz Reference SA-11S3 is an incredible sounding CD/SACD player. Had many  exotic type players over the past 30 years and the Marantz Reference SA11S3 sounds so accurate and natural. Built like a tank “38 pounds” . I am very happy with it. It saved me tons of money when selling my other players costing up to $25,000 in other digital setups.  In fact I would buy another Marantz SA-11S3 in a heartbeat for my secondary stereo system but they are so hard to find on the market in mint condition.