What would be an upgrade over the NAD M51 Direct Digital D/A Converter?

Try to demo the Ayre CODEX at ~$1750, and sometimes they pop up on here around $1500.  

I have not A/B'd your DAC with the CODEX, but if you are looking for an engaging sound, the CODEX is a great place to start demoing.  

You will want to audition the Schiit Yggy for Redbook.

Benchmark Media Systems DAC3
used Bryston
Cambridge Audio Azur 851D
Mytek Brooklyn
Auralic Altair

If you have - say 2,000 Redbook CDs - and a couple dozen high bit rate downloads, SACDs and whatnot, then you will perhaps have the fun task of thinking about whether it is better to get a better Redbook DAC or a better DAC for 1 or 2% of your collection...

I'll be curious to hear your thoughts on the comparisons.  Be sure to address any ground loops, etc. ...

I would chat with Alan at Hi Fi Buts in Atlanta.
he carries NAD, Aesthetix, ARC, Brinkmann. primal Luna, Ayre... lots of DACs that people are mentioning...
the Yagi is direct from manufacturer - and I recommend reading the book also !!!