In the first week, the Mormon airforce rises into the air and starts a carpet bombing campaign.
Seemingly, the Amish are destroyed as there are no signs of fighting back. The Mormon missionaries move in to pacify the newly conquered territory. But all the towns are dead and empty.
After two weeks of raising the Mormon flags everywhere, the top brass gets a notice: several Amish towns have sprung up in the hinterlands. Quickly the Mormon army rushes in but all they find are desolated settlements.
General after general gets burn-out from this game of whack-a-mole. The Mormons want a fight but the pacifist Amish aren't playing along. The Mormon youth gets dissatisfied with their rulers who called then into a war and are not delivering.
On the other side of the curtain, the Amish are not allowed to fight back. They simply leave their homes and rebuild somewhere else, especially in places the Mormon army just left.
But some amongst them are of the opinion that, although fighting is strictly prohibited, a few accident should be within the rules.
So the numbers of unexplained explosions in the Mormon homeland start to rise. It's just the beginning, but the methane tanks on the Amish dairy farms overfloweth.
A Mormon officer suggests arming local cheese lords to get a hold of the situation. Wherever have we seen that before?
My only proposed time dit: Due to their uncanny ability to construct elaborate building in a single day, the Amish continue constructing full barns and houses at each site.