Update: my friend and I had to roll back to HQ 0.45.4 to make it work, but by creating a scenario in the briefing room, deploying forces to the scenario, and either starting or joining a game, you can both deploy your TO&E from HQ to MM and get it back at the end of the match with all damage and glory intact. For some reason, 0.46.1 will not let you join a game from the briefing room.
That path eliminates all manual MUL bookkeeping. We're excited to say the least.
I'm continually amazed at the level of detail put into HQ and MM.