Patrol missions and sorties anywhere but Sol or Delta Serpentis.
I want to see what's going on in FS2's colony systems around Capella, see the BP universe outside of the front lines of war. I doubt the GTVA committed ALL their fleets to Sol (that would undermine their ever-vigilant Shivan defenses) -- I want to see what's going on with the other ones. See firsthand what the years have done to the GTVA colony systems.
EDIT (too many times): This is not to the exclusion of other ideas. I really like the Reverse Delenda Est idea. A lot. I suggest presenting the GTVA side as You Are Alpha One, with no characterization or dialogue, just as you were in FS2. Alternatively have it as an Alternate Reality Storyline -- you get to change history, kill Laporte and co., crush the UEF once and for all? Of course, that means we might be doomed, but hey, at least Alpha One will get to die gloriously in battle against the Shivan armada.
EDIT 2: A crazy twist launching point would be if the Imperieuse (and you) don't make it in time and the UEF actually succeeds in getting the Carthage (although I admit this is farfetched since the BP GTVA is quite precise)