There's a game that can give you an experience that's pretty damn close, though it is set in a steampunk/dieselpunk world rather than space.
I give you Guns of Icarus Online. It's a multiplayer game where each team is divided into crews of four, who must work together to operate a massive balloon-powered airship.
Captaining a ship in GOIO is a lot like flying a large frigate in Starsector...except that your guns and shields, instead of being operated by you or the AI, are being operated and maintained your human teammates, who you have to direct by giving orders.
It's a blast guys, go check it out on Steam. It'll be on sale for 9.99 for a while. And while you're at it, back the kickstarter for their Adventure Mode, where they will be introducing a dynamic world environment which will provide players with missions, pve, progressions for their characters and the world itself.
Since there seems to be some interest from the community, I'm going to start a list of Starsector players who play GOIO, so we can find each other in game! Just reply to this thread with your GOIO name so I can friend you, and I'll see all of you in the skies!
Starsector Forum Name: GOIO Name (Steam Name if different)
Graidon: Audie Murphy (Zwerchau)
http://www.kickstarter.com/projects/musegames/guns-of-icarus-onlineadventure-mode