In continuation: Been root'ing (pun intended) around some more in the database.

It looks like /fridge is everything important about the device. So far, I see one table that appears to have the serialno value that identifies the device. In theory, I think updating this value to the target eDGe's serialno may make the backup restorable to a different edge.

** DISCLAIMER ** Completely untested by me, since I do not have a second edge for the purposes of research or torture. I'm only reporting what the data suggests may be possible. Your mileage will vary. Make sure you have an entirely separate backup and are willing to do a factory reset. I apologize in advance for the mayhem that will probably ensue, but I did warn you, right???

Requirements:
Be able to move a backup file to another PC.
Be able to run zip and unzip to uncompress/recompress the backup on a PC.
Have and be able to run sqlite3.

1) Determine the device ID/serialno of the TARGET edge. This is the serialno with the barcode on the "binding" edge of the closed edge like this: F303082002AF (No, not my actual serialno).

2) Do a backup on the source edge.

3) Copy the backup to another PC, unpack the zip file.

4) go to /fridge/.edge/.esi-data/.databases

5) run sqlite3 library.db

6) in sqllite execute the command: update esimeta set device = 'F303082002AF' where _id = 1 ;

7) quit sqllite, and rezip the directories /fridge and /sdcard (or /extsdcard if that was unpacked.) Alternatively, you may be able to just freshen the zip archive with only the library.db file

8) move the backup file to the target edge.

9) try to restore, cross fingers, get ready for disappointment, etc.