Well, if your host walks on water and can do no wrong, and you've done everything suggested in the FAQs referenced, then ... I guess you have no options other than what you suggested.
Once Zen Cart passes the email to your email server, it's up to the email server to do the delivery. Zen Cart offers several options for the various kinds of email servers commonly in use. You need to find the right one suitable for your particular server.
As for database backups, there's a backup contribution in the downloads area, making backups quick and easy for most hosting server configurations ... and it's a whole lot faster than the other one you mentioned.
I hope you find satisfaction with your choice.
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