|the water stained ceiling|
See, the reason we hadn't addressed the leak up until this point is that there was no water coming through the ceiling, and the water stain hadn't really grown. So Adam stayed downstairs, I was upstairs in the bedroom by the access panel, and I finally saw water.
Very slowly, drop by drop, water was coming from the center pipe behind the shower.
You have no idea how relieved I was to find that this would be the source of the problem. Since we already have some clear silicone to caulk around the faucet, this is a free fix. No expensive plumber needed. We will have to replace the drywall from the ceiling (there was some mold obviously) but that is something we would have had to do anyway.
So now we wait for the shower to dry out, then Adam will caulk it with the silicone, then we can test it again to make sure no more water is coming through.