note that you probably need to trust the remote household with your data

Probably not actually. Borgbackup (and any sensible encrypted backup system really), does client side encryption. So the data should be encrypted before it’s even sent down the wire. The remote household shouldn’t be able to access the data without the encryption key/password.

I mean, they will have to trust the remote household not to destroy the data, but that’s pretty much an unavoidable limitation.