Managed to chop out the rest of my project and make a tiny example for what I want to do here. When you press M, the layoutscale changes to zoom out (or in) and the camera (invisible sprite that'll follow the player) also moves, to keep the bottom left corner of the stage completely aligned with the bottom left corner of the screen.
It... pretty much works. But it's a pretty choppy transition, as you can see. Can anyone think of a better way to do this that would look better while it's moving?