OK, some success:

As you all probably know, the full backup initiated from the UI creates a bunch of zip files in ~/MyDocs/.backups/BackupX/

Misleadingly, the messages aren't actually stored in messaging.zip. It turns out almost everything I care about is in contacts.zip. There's a file called in contacts.zip under Root/home/user/MyDocs/.tmp called trackerbackup.

This SQLite database appears to hold all the contacts, SMS's, and as far as I can tell, even the calendar entries.

Creation of this file is triggered by the backup-framework invoking /usr/share/backup-framework/scripts/backup-essentials-tracker-backup.sh.

I still haven't figured out how to auto-invoke backup-framework itself, other than a string in the binary saying "Backup-Framework is launched from SSU, no UI update" (SSU being "Seamless Software Update" -- presumably such as a PR update). This indicates to me there *must* be some way to invoke it in SSU mode...somehow...