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

I am looking for some advice as to an upgrade over the NAD M51 DAC.  The objective would be to get my digital end to be more engaging so that there's less of a gap between it and my vinyl front end (Manley Chinook pre, Technics 1200 GAE).  

Would this necessarily require me to spend >$2k?  I'd be fine going used.  I have a Primaluna Dialogue HP integrated, so the replacement DAC doesn't need to have an independent volume control.  

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 !!!
I hate spell check
make that...

Hi-Fi Buys 
These are great suggestions!  Thank you. I'm off to start research based on your help.
Of course every component may not mesh with you gear, but that is a tough dac to beat.....prepare to spend $$$

I use one for and number of sources and it sounds pretty good given its price....
jb:  I use a Cary DAC200ts in one setup.  Just using it for CD and Tidal, for now.  I think it sounds pretty rich and engaging, with upsampling and tube output.  Although lose some detail that way.  If that's not where you want to go, might not be that much of an upgrade over the NAD, if at all.  May be even a step backwards, depending on your preferences.  Probably could find one used eventually for around $2k-ish.

A Schiit and a NAD M51 are on my short list whenever I get around to upgrading a different DAC.  So, for selfish reasons, I'd recommend you try the Schiit and report back on your thoughts on how it compares to the NAD.  :)
You know you're right. It may be tough to beat this DAC without dropping a fortune. I may just need to realize that my analog front end is just better and my digital is very listenable just not going to be as good. 
Try a stand alone preamplifier. after trying the Auralic Taurus pre i couldnt go back to using the M51 as a preamplifier
I upgraded from an M51 to a PS Audio DirectStream DAC when it first became available and haven't looked back.
The DirectStream DAC does not use a conventional DAC chipset, instead uses an FPGA, so once or twice a year PS Audio makes firmware updates, once installed, improves the performance of the DAC, something that is not typically possible with a DAC with a conventional DAC chipset.
No plans to replace the DAC, from someone who tries stuff out and does lots of upgrades.
Added an Innuos ZenMini to the NAD M12 Analog/Digital/Streaming Preamp which is based on the M51. 

It got very close to the PSA DirecStream / Auralic Vega G2 that i also was demoing. 

My conclusion was that, what ever DAC/Preamp i end up getting i need to have an Innuos as source. Just a question of which. I have tried various combinations with the following products  Lumin T2 , Auralic Vega G2, Pirmare PRE35 Prisma, NAD M12 w. BluOS, PSA DirectStream w. Bridge II, Cambridge Audio Edge NQ, PSA Stellar Gain Cell, Simaudio Moon 390.