@bmann Yeah, in that case, I'd say just use a provider that allows you to buy extra storage inexpensively and mount it as a volume. BuyVM is the one that comes to mind honestly.
You can also use CIFS or NFS, but I don't know how well I'd trust them as primary storage for an app.
Also, as said, some apps support external S3 (although that limits your capability to fully encapsulate your backups).