After one humiliating loss where every single race were obliterated one by one by the unstoppable swarm of the Thoraxians, I finally managed to win. I started on the Thoraxian homeworld (yay) and made damn sure that everyone hated their slimy guts, so they were kept in check. The Burlusts tried to rear their ugly heads around and managed to wipe out the Peltians before the rest of the galaxy said "Dudes, stahp!"
I won by bombing the everliving crap out of the Thoraxians and the Burlusts. Getting the other races into the Federation took some work, but not that difficult overall, to be honest. Is it just me or does that "orbital bombardment" thing just work a little too well?