Okay, so here's an update. Got some 50 ohm Sennheisers on sale, and whaddya know, no more volume problem with the Stomp. With the 80 ohm Beyers, I had the volume knob all the way up and it was still too quiet. Using the Senns, I only have the knob at 50% and it's the perfect volume with most of my presets.
I'm really glad I got these instead of the 250 ohm Beyers I was also considering. I'm guessing they would've been even worse with the Stomp than the 80 ohm pair.
So at the end of this whole saga, in this layman's opinion, if you've got a Stomp you want headphones with less ohms, not more.