I keep the toons whose mods are borrowed by the "KAM team" in a few squads. When I'm done I just click through them and reapply. It's still a chore but at least I don't have to go through the whole roster, look for whoever is missing mods and reload them.
So with that system, what would help me the most, and relatively easy to implement, would be two buttons at the squad level. One creates a tab with 5 loadouts from the squad. The tab name can be generated and saved along with the squad for later restoration via the other button.