Keeping (Partial) Backups Small when using SQL Server FILESTREAM
The problem this caused was that the log file (which also gets backed up) is now unnecessarily large because it includes the FILESTREAM data.


I'm not sure if you mean the log file itself is too large or that the log file backups become too large.

If it's the former then how often were you backing the log up? Depending on the application design you may be able to reduce the size by backing up more frequently (and every 5 minutes is not too frequently). However if you were already doing that and it was still ballooning then you're probably out of luck. Why is the large log file a problem again?

If it's the latter - it sounded like you were happy to continue with simple recovery model and no point in time restores if it let you have smaller backups; in which case stay in full mode and discard your log backups.