Upgrading to a stand alone DAC

I will add to the Schiit Bifrost 2 recommendation.  I have the same NAD CD player as you and was simply stunned at the improvement made by switching to the Bifrost 2, which I later upgraded to the 2/64.  Better tonal quality of the instruments, better soundstage, better bass definition, and better definition overall.  And, it is only slightly more than half your budget.  A used Yggdrasil at closer to your budget most likely would be a further improvement.

I’d like to second the Bifrost 2 recommendation.  I went from using my NAD C568 CD player to the Bifrost, which I later upgraded to the Bifrost 2/64.  I could definitely tell a difference moving from the internal DAC in the CD player to a a stand-alone DAC.  The upgrade to the 2.64 added a modest improvement.  I can only imagine that the Yggy by Schiit would be yet another step up.