OK..this has been a couple years in the making, but I think I finally have something ready to distribute. In our environment (probably like yours to), the users don't have admin rights (which means they cannot run Apple's Migration Assistant), so I had to come up with a method for an end user to backup/migrate their data to another computer if they want. Designed to be run from Self service....
Source Code: https://github.com/ScottEKendall/JAMF-Pro-Scripts/tree/main/MigrationWizard
We use Microsoft OneDrive for our environment, but it can be used on SMB (legacy) networks as well...I used the tar method of backup, but can easily be adapted for rsync if you want to use that...
If you want to add/remove items from the migration list, it can very easily be done using the JSON blob construct (details on my website).