There's a fleet out there called STFRaiders. They are split up into a Starfleet and Klingon fleet. From looking at their forums I'm thinking about applying. They formed to do STFs. As I understand it, their application requires you send a pic of their build and do a tryout run with them to see if you're experienced/well equipped enough.
Check them out, it sounds like they may be up your alley.
Gemini Fleet Command is interested in new, up and coming, and experienced Captains to join its ranks for all aspects of the game but in particular STF's. We have been around since the beginning and are just starting to fire back up again with the advent of F2P.
We are a casual fleet with Forum Roleplay and option. We use TS3 or vent and welcome Captains from all corners of the galaxy.