Well, these things adjust with a twist. Maybe I could twist it without having to take the whole thing apart.
This seemed like a good theory.
At least, until the top of the valve came off in my hand.
Water sprayed out through the opening to the ceiling. I tried to jam the cap back on and failed. Then I started grappling with the shutoff valve and got it down to a dull roar. This allowed me to get the cap back on.
Interestingly, the valve now appears to be adjusted correctly, or so it did after we cleaned up the water from the floor and ceiling.
I think I may end up replacing this valve shortly.