I wonder if the stack save preserves position.
For what it's worth, when I transition from overworld scene to my battle UI scene, I have to store the actor's position and then restore it when I load back to the overworld map. I'm not sure if there's another / better way to handle it, but that's what I'm doing when I restore the stack. I'd imagine that for a platformer / metroidvania it's a much bigger challenge since you could have a lot of enemies per scene to keep track of.