Most shared web hosts do mention in their terms and conditions and fair use policies about not using the storage for backup purposes, mainly because most hosts oversell storage in order to make a profit. However if people are using the storage for holding backups they're more likely to use all the storage space allocated to them reducing the amount the host can oversell.
It's why I'd recommend getting either a VPS or dedicated server as you can then have full reigns of what you store.
Thanks a bunch for your help. If Kimsufi's least expensive dedi ever becomes available again, I'll grab it and give your script a shot.
Thanks for everything!