There is. Back up your SMS. Email yourself, attaching a copy of the SMS backup file.
Considering Drive's recent size limit for free accounts, you may want to rethink how you're backing up your SMS, because you can run out of space just with daily SMS backups.
I found out the firefox workaround works successfully. At least for right now. Install firefox/sign out of SMS backup. Sign back in and when it wants to authenticate, chose the FF browser. Works as it's supposed to now. At least until Google finds out. lol.