Roofing crew showed up and inspected the roof. They discovered over six inches of standing water up there (it's a flat roof), and said I was in danger until it's cleared off. They managed to get the drain open again and cleared it out. I took a video of the water flying out, which I'll post after I do some minor editing.
They recommended replacing the roof entirely, and are going to give me a quote to that end.
Ugh. I wasn't planning on spending that much money right now, but I guess I'm lucky enough to have savings for this kind of thing.
The social network of the future: No ads, no corporate surveillance, ethical design, and decentralization! Own your data with Mastodon!