Okay, after:
1. uninstalling OXCE
2. removing all the folders in my data folder (which is on my SD card) except mods, UFO, and TFTD
3. Briefly panicking because [internal storage]/Android/data/org.libsdl.openxcom appeared to be gone, and that was where my saved games and config file were
3. reinstalling OXCE 7.7.3
4. Launching OXCE
I am now getting a "failed to map common" error, twice, followed by the folder selection dialog (which remembers everything), and the org.libsdl.openxcom folder seems to have reappeared along with all of its contents. The errors and folder selection dialog appear each time I run OXCE now.
I checked in the folders to see what's going on, and found that OXCE didn't recreate the common, standard, xcom1, or xcom2 folders in the data folder.
[Copy UFO Data From Directory] and [Copy TFTD Data From Directory] don't appear to do anything but I don't remember if they're supposed to.
[Save and Restart] crashes instead of restarting, but it always did on my phone, and that never stopped OXCE from working before.
Edit:
First, I just realized that the saves that were restored when I reinstalled OXCE aren't the same ones which were there when i uninstalled it. I don't know where they were hiding, but they're old ones. I had to restore the correct ones from the backup on my PC.
Second, I just got 7.7.3 working properly (or, no errors on launch, no errors when trying to read reports, I haven't tried anything else yet but that's all that had broken) but to do it I had to manually extract the 1_standard.zip and 0_common.zip files from the apk, then extract the standard and common folders from them, then move said folders into the OXCE data folder.