Ooooooo, be careful. I've been through this especially wth the diskspace problems that you mention.
If you delete a backup before you have a new one and the backup job continues to fail, you will eventually end up with no backups what-so-ever. Like you said, break the backups up and don't delete a backup until you're sure that you have a new one to take its place.
--Jeff Moden
Change is inevitable... Change for the better is not.