The vet called me back this afternoon to let me know that I need not worry-- even with blood in the stool. And she prescribed some medicine for Meester Max. I asked if this was treating the symptom or the underlying cause, and she said the latter-- that she thinks he has a bacterial imbalance. So for 10 days Max gets a dropper of meds twice daily.
I just gave him his first dose. I'm fairly certain that Beatrice was on the same meds (or it might have been Zoe and/or Malcom). But Max likes it a whole lot less. He was lying in the sink, so I popped the syringe in his mouth no problem, but apparently not far enough back into his mouth. He sat up and managed to spit some of the medicine out. I didn't know cats could spit! Then he shook his head a bunch and he looked like he was foaming at the mouth. It was hilarious but alas, there I was sans camera.
I cleaned him up and we'll try again in the morning with dose number 2. (I don't know how much he got into him, so I'm not willing to give him more tonight.) I'll update you on his gooey poo (don't you feel lucky??) as the meds take effect. (I asked the vet tech who gave me the meds how long 'til I should see signs of it working-- she said it could actually take up to two courses [20 days] of the meds, so we'll see.)