Not uploading to the Amazon drive, but to S3 - maybe possible to adjust upload routine...
I wrote my own little script to do account (not system) backups and upload to S3. They run via the root crontab and can handle daily, weekly and snapshots with different retention periods. I needed not only full backups, but (for cost and bandwidth reasons) also incrementals with different retention periods - downside is that it is not cpanel integrated and requires some script updating, and it is not 100% perfect yet (e.g. e-mail notifications are missing), but it is free
Feel free to download here and use/share as you like http://managed-hosts.com/s3
Put both files in a /home/tools directory and adjust both and the crontab as needed.