Welcome Pathogen,
I remember having trouble with the Khan scenario also. You probably could go to 'Multiplayer' and 'Host' and create a game under the scenario name 'Wrath of Khan.' Then, add an AI player for Team B, who will be Khan. It is the same as the single player one, but is made to have two human players-- so if you set the opponent as an AI, it will try to attack you, instead of ending the mission.
The scripted missions in OP are only available for the Orion Pirate cartels, and for them only after you have flown around a little bit. If you want some more interesting missions, search this site for Evil Dave's Warp missions. They are a lot of fun.
Good luck!