Since no pre-defined reports are available, and the Contacts system table, although it contains all the necessary data, cannot be queried or exported for some reason, does anyone have a workaround so I don't have to manually pull the Mobile Connect deliverability report every day? I'd really like to automate the process for the client, and for us.
If the MobileConnect deliverability report you're referring to is the SMS Detail Tracking Report in Data & Analysis -> Reports, then you can schedule this report to be e-mailed to one or many e-mail addresses at a regular interval.
You can also have the report saved to the enhanced ftp.
So instead of running the report from within MobileConnect, you need to head to the Data & Analysis -> Reports part of the app, which is separate from MobileConnect.