I'd just dig them up, leaving as much soil around the root as possible, and relocate them as one piece. I've sccessfully divided peonies in the spring but it's always been really early, not one buds have formed. Just treat them like Amy other newly transplanted perennial and they'll do fine. You might want to set up a bit more shade until they're established, though, and don't let them dry out completely. I wouldn't cut them back but you might want to remove the buds if there are many. Congratulations on your new peonies!
