Not enough warriors to defend all your borders? Or are they too weak after the Gabite Officer did a number on your chances? Well, here's something that could be useful (in fact I'm abusing it like you wouldn't believe in the ninja competition episodes).
First, make sure Avia is among your bordering kingdoms. Defend the rest of them with the best forces you have, then put your weakest floater in Avia, alone. The AI will naturally be drawn to that kingdom, and will send one solitary warrior there. If their Pokémon isn't a floater, you've already won. If it is... to be honest, I've never tried playing ring-around-the-rosie all over the map to avoid coming close to the opponent, but if I have to attempt it I'll let you know how it goes.
The idea, in the event that you're not facing a floater, is to send yours straight to the top left island of the map. It's completely impossible for anything that doesn't float to actually STOP on that island, since whichever spring pads send you there immediately put you on another spring pad. Just stall out the 20 turns, watching the AI desperately try to get to you and failing miserably, and you've won.
Now, I'm not sure how reliable that method is when you share borders with several AI armies. Can you get invaded more than once per turn? It's never happened to me at all, so I'm not sure. Nonetheless, the point of this post was to give you a basic idea of the trick. Deeper intricacies are something you may have to find out for yourselves.