I moved a tree peony in the spring. Several people told me it could not be done successfully. But the option was move or it was going to be destroyed. It struggled the first year. Was happy last year (the second year) but did not bloom. This year (year three) it is very very happy and I'm going to be blessed with one bloom.
As for herbaceous peonies, I have had people give me them in the spring. It has taken mine anywhere from two to four year before they bloom.
It can be done. You just have to be patient for blooms