CD Player advice request...

If you already have a decent CD/DVD player as a transport, save yourself a lot of money and get a Beresford DAC. The 7520 model is already advertised on this site, but for the top of the line Caiman model, you have ask Stan Beresford nicely and he may send you one. He can be reached at info@homehifi.co.uk. The Caiman is a VERY limited production model that is hand-built and tested, all for about a quarter the price the Benchmark USB DAC-1.
I had a Benchmark which I liked very much, but to be honest, the Beresford is better with a bigger and more natural soundstage, more detail, better vocals. It is simply more musical. My transport is an old Panasonic DVD player, but that makes no difference with this little miracle. You will probably have to wait to get one, but trust me, it's worth it!

bryston bcd 1....late to the party, but they got the 'natural' or 'neutral' thing 'right'.

Have you considered a used Ayre CX-7e CD Player?

Most any recent vintage, decent, jitter resistant vintage transport, CD or DVD player, or other digital source with digital output feeding an mhdt Constantine DAC could meet your requirements. I use a 4-5 year old Denon player/recorder that cost $600 originally with mine and have also used a 6 year old Marantz DVD (see my system listings). A used mhdt Constantine can be had for well under $500 used.

An mhdt Paradisea tube DAC might do it also but might be a tad warm for your requirements with the stock GE tube on many systems. Other model inexpensive replacement tubes can remedy that if needed.

Ayre and Gamut out of my price range...
My CD player is unreliable so a better integrated transport/DAC combo is my preference.