Personally, if I were you, I'd consider leaving the db in simple mode while clearing out the old audit information, assuming you are deleting in batches. Then you wouldn't have to do a tlog backup inbetween each audit batch.

Do an incremental backup when done with deletes and go back to FULL mode then.

Btw, I suggested clearing the logs immediately also because it will give you space to back up other logs to, even if that's not the drive where you normally store log backups. If the log backup is just an intermediate file, it doesn't really matter where it goes on disk (other than overall performance, but that is secondary right now).