The thing is, you will need a lot of events (maybe some coding, but not sure, haven't tried). My method of thinking the best way it would work is for there to be a couple of checkpoints (not totally sure on setting these up) that you MUST fly the plane under in order to do the next checkpoint. After flying under all of them, you can cross the finish.
I also think that your weapons should include some kind of grenade launcher (explodes on contact with vehicle) and Kaje's sniper rifle (I think it's his at least) for picking people out of planes. Also, Ephialtes' sawn-off shotgun for destroying planes.
The plane used should be a stunt plane (faster, easy to control for most people, compact, quick reflexes).
Being on an aircraft carrier, there should be water. Anyone who touches the water outside of their vehicle is killed on contact, and either respawns and has to start the race over, or just has to spectate until win/last man standing.