Thanks, doing the factory reset seems to have fixed it (or, well, any number of other potential variables, but that was the new thing I tried), and I’ve now been able to update to the latest firmware. I then had to do another factory reset to make the app properly talk to them (i.e. getting the battery status, etc), but now it seems reliable so far.
(I was also personally fine with using them even without that, so I wasn’t too worried, but it’s good to have them fully working again)