Hello and welcome, peonies generally are tough. I've moved mine more than once to get them out of deepening shade. I have heavy clay soil here in VA. so I add compost and sand when I replant. Don't bury the eyes more than an inch. Cut away and get rid of the old folliage every year to reduce the chance of blight.

No matter how careful you are, you will probably wind up with more plants than you started with. Replant everything that has an eye. In a few years that single stalk will be a healthy blooming peony with many flowers. If you have too many of one kind, you can trade for others that you don't have.

Keep in touch. Let us know how it goes.

I think in your zone, 2" is the recommended depth for the eye-it is in my zone and you are colder. After the soil freezes, cover the spot with a layer of salt marsh hay or other non-packing mulch to help prevent heaving.