Tree peonies can take severe pruning. You can cut the plant all the way to the ground it you want to, it will come back, no problem. I don't know how much that will control the size though. You have a very well established tree peony. It looks very happy. And is gorgeous.
You could graft the heck out of it this fall and end up with more plants too. (We have a grafting tutorial on this forum.)
I haven't ever actually split a tree peony. So I can't speak to that. I have moved one once,with little disturbance of soil and it barely made it....but it did. So that is a possibility for fall as well,
Welcome.
