It's not the OS; I can edit using Chromium. Chromium is locked down a little less tightly than Firefox, but it's pretty tightly locked down. It's running HTTPSeverywhere, so that plugin probably isn't the cause.
Has anything changed on the server side that could have broken my editing?
I get nothing; Potlatch2 just doesn't start. ID doesn't either. Is JOSM a variant on the viewer? That's all that displays there.
An interesting note: If HTTPSeverywhere is disabled, ID starts, but Potlatch2 doesn't.