I'm not a complete failure!
Mom ordered me to replace the ring, although I managed to convince her to let me just buy the ring now, and install it after I applied to grad school.
Good thing, too!
There were dirty puddles on the floor.
I didn't notice it moving, but it sure did when I kicked it! I popped a cap and the bolt wasn't even finger-tight. I happened to have an 11mm socket handy that I found in my room. It fit pretty well. I tightened one side 5 full rotations and the other 8.
I don't know the torque specs for plastic and porcelain, but I stopped as soon as I felt any resistance.