It's possible the rivet head you see in picture 3 is the top of a post that goes into the back casting, but I think it's there to hold the stack of lamination that make up the stator together. I suspect the stator is just pressed into the casting. You may have to make a custom tool to remove it.

I would suggest getting a short section of pipe that fits freely over the stator and rests on the edge of the back casting. You would place a plate on top of the pipe and it would have 4 holes for threaded rods that would go in between he coils. The threaded rods would have projections that would reach under the outer sections of the stator and lift it out as you tighten the 4 nuts evenly.

Another possibility is to chill the whole thing in a freezer, then quickly heat the outside casting with a couple of torches and it may expand enough to just fall right off. This often works great for getting bearing races out of aluminum housings, but this one kind of looks like cast iron to me. You don't have the difference in expansion coefficient working for you, so you have to heat the outer part quickly before the heat penetrates to the inner piece (and you have to be careful not to damage it).