My theory was that the problem was a clogged showerhead, rather than some sort of plumbing-wide problem, since my water pressure was fine. Sure enough, when I ran the water through their shower with the showerhead removed, the water pressure was great — and I noticed some black rust and corrosion around the inside of the pipe, and inside the showerhead itself. There was a small screen where the showerhead connects with the plumbing, but it was so full of corrosion that hardly any water could make it through!
The solution — I scraped out some of the corrosion inside of the pipe, and ran plenty of water through it with the showerhead removed, to try to ward off future clogs. I also soaked the showerhead itself in CLR, and cleaned out the screen with a scrub-brush.
I replaced the showerhead, and voila! Water pressure good as new.
I’m just glad that it didn’t involve a plumber this time 🙂