Sorry for being late for the party...
Yeah, "all teams at war" is the way to go for what you are doing... additional IFFs and IFF-flags I would not touch unless you are extending the number of teams beyond the original 3 (friendly, hostile, neutral)
However FFA-type missions are a difficult piece of balancing; you will have to account for player interaction with all teams and for the interaction of the AI with another ... the mission can go really off rails if the player focusses too much on one team and not on the others...
Also the retail AI doesn't take well to fighting at two fronts unless you stricly guide them ... AI ships target the next best threat and not all enemies equally; which forces you to really guide them from target to target via events (its manageable, don't worry) unless you are going for "clumped together in a single furball"