Sorry to hear that the issue persists. You mentioned that the "backup settings are working on your previous host." How can they be working with the same URL, if your current URL is pointed to InMotion Hosting's URL? Did they use a different URL, or were you simply stating that they work previously?
I did some further looking into the error message that you were seeing and it is defined in the Moodle documentation: Automated Course backup
Basically, the error messages you're seeing indicate that there are no problems with the backup. Checkout the article's error message definitions. If you think that a problem still exists, you will need to go through all of the settings for the Automated course backups.
I hope this helps to clarify the issue!