Shower mixing valve leaking

I have a Hansgrohe Ecostat Pressure Balance Trim S valve that's leaking. The dripping is coming from the shower head — about 1 drip a second. This problem started when we replaced our hot water heater, during which we played with the screws behind the trim. We've since tried to play with the screws again, but to no avail. It's possible the leaking was happening before the hot water heater was installed and therefore a red herring. It's also possible that the new water heater has a bit higher pressure and caused the leak to happen. Or maybe we just unseated a seal of some sort.

I'm not sure what to do next. As an extra obstacle, there's no shutoff to this unit or fixture — I'd have to shut down the whole building (it's an old building with poor plumbing design). So I'm ideally looking for a fix that can be done with the water on.

https://www.hansgrohe-usa.com/articledetail-ecostat-pressure-balance-trim-s-04233000 has more details on the fixture.