Can I change my state of residency from one school year to the next?

You need to check the residency policies of each of the places you might apply to. Each sets its own policy. Some places have specific waivers for active military and their dependents. Others absolutely will require 12 months in-state residence.

Another possibility is to investigate programs like Penn State World Campus and University of Maryland University College. Both of those offer extensive online classes, and live classes on and near military bases around the world. Something like that would mean you wouldn’t have to transfer again if/when you move again.