What sort of upgrade from Rega Brio to go with my Dynaudio's X12?

interesting comment. that was my first idea, in fact. I thought of getting Monitor Audio's Silver 100 7G people talk wonders about, then was told my speakers were too good for the Brio and that I had not seen what they were able to do with more power, thus, this post and, now, A-S801 more power, very well reviewed amp, etc...

I believe you are the right path upgrading your amplifier for the X12s. I have heard and truly like them. At a budget of 'up to 2K' you can do much better than the Yammy 801 in my opinion. 

What sources are you using?

Cool. Was using Bluesound Node and now experimenting with the Wiim Pro Plus. 

Consider the Heaven 11 Billie integrated amplifier mentioned above.  Not pushing it, just very satisfied with it.

Complete with DAC and phono.  

Rich  

The X12’s are 86dB sensitivity and rated at 4 ohms impedance, I am not surprised that the Brio is not doing it for you. NAD tends to be good with current thirsty speakers. Maybe Hegel, not sure. I would watch the used market and do your research, and focus on amps that do well at 4 ohms, and sound good, of course. 😀