Finally got around to replacing the wax ring on the toilet this week. Simple enough job.
Unfortunately once I got everything back together and tested, the toilet was still leaking. The wax ring seemed to be sealing everything up just fine. Finally with a little more investigating I discovered the culprit: a tiny 5 mm long crack at the base just outside the wax ring.
I wasn't able to get a very close look at it without dumping the remaining water out of the bowl, but it looked like it may have been a manufacturing defect.
So I guess it's off to Lowe's sometime this week to shop around for another toilet. We'd been meaning to upgrade the toilets anyway...just not quite so soon.