Thoughts on DAC option

If I were you, and, because your speakers and components seem quite satisfactory, I'd start with doing some experimenting with your cabling.  Cables can make or break any quality audio system.  Happy listening.       

Vega has a pretty decent DAC section and built-in analog preamp designed to minimize distortion and noise. So I agree with all the gentlemen suggesting you leave the Vega as is and focus on the cabling instead. Refining cables to tune the sound is a great approach—it works in my system, though it does cost money. Speaking from my own experience, if someone as frugal as I am doesn’t mind spending on cables, nothing should stop you.

When it comes to interconnect cables, DH Labs and Cardas are two affordable brands worth considering. In general, DH Labs’ silver-plated series offers more dynamics and punch in the low end, while Cardas’ pure copper provides a smoother presentation. Both feature gas injection to vacuum the line, reducing dielectric constant and capacitance that sort of good stuff.  The choice ultimately comes down to personal taste. Beyond their price point, the law of diminishing returns kicks in—and it’s up to you to decide whether you want to go further down that rabbit hole.

I don't associate the Chord sound as smoothing things out. 

You might consider a network filter.  If placed before your streamer it can smooth thing out by reducing jitter.  It did for me.  Good luck.

Even if the DAC was your culprit (which I highly doubt), a Chord would be a poor choice of replacement. They are not remotely smooth or analog sounding IME. 

I wonder what the output impedance is of your hybrid amp. If it is relatively high like some other Prima Lunas, that could be your issue.