CD Player to match Classe amp and Kestrels

Classe CAP-100 Integrated Amp
Meadowlark Kestrel Hot Rod Speakers
Synergistic Research Alpha Quad Speaker Cable
DH Labs BL1 Series 2 Interconnect
NAD 521 CD player (1997)

A relative newcomer to this world, I have upgraded everything in my old system to what you see above. The last piece is the cd player, which I hope to replace for under $500 used.

I have already read the excellent posts suggesting Cambridge D500, Musical Fidelity E624, Rega Planet, and others, and I am asking now for fine tuning, if you will.
My tastes mostly run toward acoustic jazz/classical and I enjoy the musical sound of this system. I am wondering what CD player will best complement it and maybe add a little detail.

I am also wondering whether my (obviously) limited budget right now will really gain me that much improvement over the NAD. I want to replace it with something I can keep for many years. Any thoughts are appreciated.
Try to tretch for the new Rega Planet. It has all the magic of the original Planet, that is the ability to create music, and adds a bit of detail and resolution. Woudl be a fantastic match in your current system!
I am using HR Kestrals w/ an Audio Refinement integrated and the same i.c. that you have-
My cdp is a Rotel 971 with some mods and is an excellent fit in the system-
BTW I just added some polycrystal spikes to replace the stock spikes and that is a worthwhile tweak.
I would recommend an Audio Refinement Complete CD player. If you can find one used it should be within your budget. I think it will easily best the NAD 521.
Oops, I just noticed that I typoed in NAD 521, when it should have read NAD 512. Thanks for the thoughts so far.