You should have some sort of conflict between your EMH and the ECH on the bridge. Or maybe the ship's crew has been disabled and the EMXs are the only ones still conscious/alive.
Or, better yet, have the EMXs revolt and take over the ship and populate it with a holographic crew. The player has to find out what happened to the ship and get it back under control. You could spice things up by having it be a situation where "everything is not as it seems", like it seems like the EMXs went haywire, but then it turns out they had a good reason for acting as they did.
I made some references to incidents where ECHs took command of the ship in Atlas Affair, Part 1. You'd have to play the mission and speak to the ECH to find out the lore behind it, but maybe something like that could be tied in, or provide inspiration for you.