DAC to pair with Eversolo DMP-A6

More separation / clarity is exactly what the Chord Qutest will give you. Along with a bigger soundstage. 

I looked up that Chord Qutest DAC - might be rather good.  It even comes with its own USB cable.

And try the Eversolo DAC-Z10.

Get them from suppliers that take returns and a/b them

Good listening.

I think what you may be hearing is the character of your amp, which is on the warmer side and less detailed in the treble region and while the DAC in the A6 isn’t great it is on the detailed side so if this is the case I’m not sure a DAC will overcome what you’re hearing and give you all of what you’re looking for but definitely worth a try because a better DAC will still sound better overall.  That said, the Qutest might be a good choice, and here are a couple others that are more on the neutral/detailed side that’d also be worth considering.  Best of luck.

https://www.usaudiomart.com/details/650266894-benchmark-dac3b-dac-black/

https://tmraudio.com/fresh-arrivals/bel-canto-e-one-dac2-7-d-a-converter/

I purchased a pre-owned Denafrips Ares DAC, for exactly this situation.  I was very pleased.  Bigger soundstage and more body.  I have since moved to another.  DAC.  I would sell my unit for $500 + shipping if you are interested.  Message me if you have any interest.