Eventually it locked me out of google on the backup phone for 48 hours because apparently I'm a security risk despite having entered the supposedly helpful security number that arrived in the text.
Which is fine, I'm sure it'll sort out. But I have a new phone on the way and I don't really want to end up going through all this again.
I'm also mightily pissed off with google and being a contrary apeth I am ready to tell them to get fucked and take my accounts elsewhere.