Unfortunately there really isn't a way to resolve a conflict without playing out the battles. If you wished to avoid that you could use the ground combat rules with space craft (sum up the PV of all the ships in the two fleets and roll dice to determine how much losses happened) until one side or the other was defeated. I think there is some sort of resolution system to sort out two NPRs in one system that you could look at as well.
But really the point of starfire campaigns is to generate interesting battles to fight out...
