Blatantly copy the looking for group system from Dungeons and Dragons Online. It is the best one I've ever seen in a MMO and unless it is somehow patented and/or EA is afraid of Hasbro it could be implemented easily without affected game mechanics.
this would actually be perfect IMO. combine it with ability to port to instance (not be ported to it automatically, but rather use a fleet pass or allow someone who's already inside (or right outside of) the flashpoint/instance send out shuttles for the rest) and it would be exactly what this game needs. no random grouping, no automatic anything. but still a system that allows for more convenient group finding.
in case people are wondering how it worked - you could either list yourself in a dungeon finder for specific dungeons and wait for invite, and/or look through list of available groups which would also allow you to list what roles you still need, and then you could whisper to them and get invite. it was easy to browse, easy to use, but at the same time, it still required human actions instead of doing everything for you.