I'm at the part where you have to defend the flagship against waves of attacking zeppelins carrying hordes of soldiers. I'm playing on Hard difficulty, so enemies soak up enough damage that I can't quite keep up with them, and they slowly destroy the ship's core. (I don't even want to think about dealing with this on 1999 Mode...)

What strategies are effective in this fight? Should I be saving my "air strikes" for the gunships, or should I be using them against the infantry on the decks? How do I deal with the Patriots?