[Endoperez]

Diseased, living units never heal, and get 1 point of damager/turn. They'll also often get afflictions.

Starvation only kicks in after the unit suffers from it for the second turn. So moving in, starving, and moving out is perfectly safe.

Your own fortresses "radiate" supply lines to provinces near them, so having a fort nearby could save your troops. If you have researched Thaumaturgy 2, I suggest casting Gnome Lore on all provinces near the Shinuyama capital - you might get lucky and get a fortress from a site. Mountains and wastes have better chance of delivering, and searching empty provinces is better than ones which already have 3 of the 4 possible sites.