OR (and the feds will hate this one) Fleet mark events by faction (1 hour fed 1 hour klingon) and DISABLE the other set during the events
I am usually extreme pro-KDF, and that still sounds wrong to me.
Make all of the current attackers neutral enemies and make them cross faction, or make the enemies "rouge" attacks, as in Klingons attacking a Fed starbase, the KDF sends people to help the feds because the attacking Klingons are criminals and don't work for the Empire or something.
Cloaking generators break down at first sign of language.
Or maybe just change the que setup so that at the end of a five minute period, whoever's que'ed, regardless of how many, start, and new players entering the que go straight to either the most recently started one, or to the next one, if none of the availables is still in round 1. (round 2 for Starbase Defense). New arrivals won't pick up as many FM's since they're already awarded piecemeal at each stage, but it would eliminate some/most of the wait times that result in people going offline or elsewhere, and for the "Sooper L33tz" out there, there's bragging rights for pulling an entire event with,say, only 3 players instead of the usual minimum of 5.