Inheriting Time Machine and merging old history
After I posted this question, I thought of a possible solution.  And it turned out to be the right one.  It's the same command!

After running

# sudo tmutil associatedisk -a "/Volumes/Macintosh HD" "/Volumes/Time Machine/Backups.backupdb/My MBP/Latest/OWC Aura SSD"


I did the same thing with the old Macintosh HD backups:

# sudo tmutil associatedisk -a "/Volumes/Macintosh HD" "/Volumes/Time Machine/Backups.backupdb/My MBP/2017-09-26-102523/Macintosh HD"


The -a flag is important because it associates all backups with the same disk identity in the same way.

The result is that all the backups on my Time Machine Drive are associated with my MacBook Pro, and that's just how I wanted it.  Once I ran these commands, Time Machine was able to delete the oldest backups and do a new one.