OK, this seemed to work just fine.
1) Clear the DLM Controller Hardware ID from AMC (bottom of page hyperlink to clear hardware ID).
2) On the current-DLM controller use Application Group Licensing form to make a note of the GARID, then clear the GARID field and set DLM from Yes to No.
3) On to-be-DLM controller use the Application Group Licensing form to set DLM to Yes, and enter the GARID.
4) Sync new DLM controller with the AMC, by saving it
5) Go into Network Elements on the new DLM controller, choose every node which belongs to the DLM and click sync.
6) Only choose Application Group Licensing and synch/commit/save.