I got 3 of those air kill missions with only 2 Tier 3 ship in roster. BTW getting Destroyer is not that hard to do since you can unlock one in tier 2 and you need to play with the cruiser that unlocks it to unlock the tier 3 cruiser than unlock the first BS.
Only way to really kill air early game is the tier 4 carrier.
I guess a way round the problem will be to allow missions to be abandoned triggering the completed mission timer without giving a reward.