Update:
Sorry to have disappeared. My daily driver laptop died. I had to replace it and attend some meetings and get some work done.
After looking at this from every angle, I decided perhaps my problem wasn't the HX Stomp, or the Headrush 108. I figured the Headrush was simply oversized for this room, and decided to try something different.
I got some small monitors; Presonus Eris 3.5. Problem solved. Through these, I get all the high end content I expect and the amp models sound like they should.
I don't know the theory behind all this, but the Headrush really wanted to be louder.
The HX Stomp still pushes more bass than Helix Native through Xsonic Interface into the same speakers, but is isn't causing the drowning effect through the Presonus monitors like I was having with the Headrush. I can dial that out now.
So maybe it was a perfect storm of the Headrush only opening up at a volume I didn't want in this room.
All I can say is I am pretty damn happy now.