So... I thought there were three, maybe five invasive nymphs in there.
Today I took the goat skull out and shook it over a bucket, and no fewer than seven American nymphs fell out. Caught those, put them in a container, shook the skull again, and more came out. 20 minutes of shaking and a small amount of poured water later, I had 30 roach nymphs in my container, ranging from tiny newborns to ones almost an inch long.
Shook the skull until roaches stopped coming out, then did the same with the driftwood, then removed the leaves and caught every roach that had nowhere to hide. Total was 47 roaches, and a few that got away.
Turns out they've been coming in a hole in the back of the lid, into the filter compartment of the aquarium, and then into the main enclosure. I've put a Vaseline barrier along the inside of the filter compartment, just on the enclosure side, so any remaining ones can get out and not starve but won't get in with the roaches I do want. Gonna put a bottle funnel trap in there tomorrow and try to catch the last few, but at least I've thinned 'em out.