I know I'm a complete noob here, and I can't claim to have any real knowledge of the coding and what not behind the game, but... would it not be possible to have some sort of Mirror Universe counterparts of all the ships currently in the event (so if one of the 5 players is on the U.S.S. Avalon, there would be an I.S.S. Avalon with the same ship type/name/registration/etc, but Terran Empire decals instead).
I also think it'd be cool to have a story mission with the Empire, one that showcases the mirror you and your mirror crew, with scars and all that loveliness, but that'd be much harder to implement. The Participant Mirrors I proposed initially should be relatively easy to code in, from my basic understanding, and would add an extra level of enjoyment to the event, I'm sure.