I would plant the tubers in pots. Moving them will most likely retard blooming for anywhere from 2 to 5 years, depending on how many eyes the tuber has.
If you pot them up, remember that container plants are more subject to freezing during the winter, because the roots don't have sufficient insulation from the small amount of soil around them. You can store the potted tubers in a cool basement or garage, where they'll be protected from freezing temperatures, but give them a little water now and then ... not much, because dormant plants can't use much. If they're too wet, they'll just rot. The best storage, IMO, would be to sink the pots up to their rims in the ground, and mulch heavily over them, (but if you could do that, I imagine you would probably just plant the tubers in the ground in the first place.
Personally, I would leave them in the containers until the proper planting time next fall, and not try to plant them in the ground in the spring.
When you finally do plant them in the ground, disturb the roots as little as possible. Moving them at all will set them back, anyway, and they will just produce foliage until they become established in the new location. Be very careful when digging, potting and replanting, because if you break the taproot, the plant can take several years to bloom again. Make sure every tuber has at least 3 eyes. Tubers with fewer than 3 eyes may not survive at all.
I'm not positive
that your peonies will survive being moved this way, but it's the method I would try.
ETA: When I had to move my peonies, I knew I wouldn't have any peony flowers for awhile, and I just couldn't imagine a year without them. I bought some container-grown peonies that were in bloom at a local nursery. I kept them in the containers, and they bloomed the following year, too. I finally planted them in the ground after my in-ground peonies began to bloom again.
"Isn't it enough to see that a garden is beautiful without having to believe that there are fairies at the bottom of it too?" - Douglas Adams