OK. I logged out of the website. I then went to the app, and did a password reset through that. Then I signed into the website, logged in successfully into the website. Then I opened the app using the "Play Now" button in the upper left, used the new password, and it didn't work.
I'm at a loss. I haven't been playing that long, so it's not like I've acquired a ton of game assets (and spend no real money), but I still would like to retain what little progress I've made.