The RME DAC is overrated . Only useful if you are into Parametric EQ (which I wouldnt recommend, get a good match instead of compensating with EQ). Nothing special audio wise, if anything has properties that are less desirable for hd800/hd820
I would see what you think of the built-in DAC first, then if you don't like it consider Musical Fidelity MX-DAC or Schiit Bifrost. MX-DAC is hard to find in USA now, but Bifrost easy:
https://www.schiit.com/products/bifrost-1
Or a cheaper route, as mentioned on other page, project horizon 3.1 (w/ golden lion) + schiit bifrost. But that isnt solid state.
Or you could go Liquid Platinum + Schiit Bifrost, and upgrade the liquid platinum to golden lion tubes
If you start to go significantly over $1000 on amp-only price because of tubes you are better off saving up for the amp i got which is $2k fully tubed and destroys everything else I have heard for hd800s/hd820