Strategically I'm thinking we should do one of a couple things right now:
1: Expand the field. They have an advantage with their weather tower, but that tower is only in one area. If we can start the battle somewhere else, say the mountains or their tundra, we'll cut that advantage in half.
2: Double down in the Jungle. This means we either try to take it out, or try to swing things a little further our way.
In either case, I think we can handle their anti-wizard stuff with only one of our two actions, leaving the other one open to improve something related to the fronts. If we design pavise shields, for instance, we should revise something for the mountains and attack there, as the pavise shields would really help us get up those open hills. A mountain rev could be something general like our armor, or something more specific like cheapen our heroism wand so we can have a squad of rough bastards to take out strongpoints or fight through breaches. A pavise shield might help in battle, too, as our primary weapon is a spear, and so our second line could stab forward from behind the guys with big shields taking longbow arrows at the front of the battle line. They could also be hide-covered to provide some assistance against fireballs.
If we go for the jungle, then I'd probably go with Revised Gale Shield to put it on a wand, and then do something like Design: Acid Fog, which, as they're happy to fight in mists, and we have wind spells to push fogs around, should be very, very fun to use.
There's also what I like, Plan C, where we surrender our actions this turn to double-down on the next, and do a Design: Theoretical for our next turn design and a stopgap revision this turn. If we can do a 180 next turn and keep them from securing the jungle or invade both the mountains and their tundra or something like that, it'll be worth it. If we do that, I want my Pegasai, as a squadron of pegasus riders with a staff of antimagic should be able to nail their tower down, and provide big advantages in general fights in the jungle and the mountains. Remember, firing up is hard and bows lose a lot of power doing that, Fire Emblem notwithstanding.