In your climate I think spring would be best. You can dig and replant at the same time and will have no problem with the watering. Al

Fall is the best time to move peonies. If I were in your shoes, I'd dig them up this fall and put them in big pots ...heal them into the ground in the fall at the new place...and they won't need much watering at all if the pots are healed in any old spot in the new yard as the fall rains will take care of that. I'd be much too busy moving in, in the spring to be digging up things in your old yard and when time permits (either early or late spring) all I'd need to do is plop them out of the pots and put them where I really wanted them into my new home gardens.