Thanks for the suggestion ... I had not considered trying to use Migration Assistant, but that makes perfect sense. I was trying to use Time Machine itself.
Unfortunately, Migration Assistant is not working for me. It sits in "Setting up" status for a long while and then the machine reboots, I log back in, and then ... nothing. I suspect this is somehow related to the rebuild of the machine using JAMF Connect. I have had lots of odd problems since the rebuild. E.g., every time I try using Migration Assistant, I eventually get a message that there's a problem with my iCloud account and I need to log back in to iCloud. This happens both when I start Migration Assistant and after the machine reboots.