There is a tree nursery near me that does pot-in-pot planting. They bury a pot, then put the tree with the pot inside. This allows for the tree to be removed from the ground rather easily and the benefit is that the trees roots don't heat up in the sun. They add an irrigation system to this and that seems to be all they do.

It wouldn't work in my zone to plant them that deep. I think 2" is the recommended depth, I tend to barely cover mine & they do great for me. I'm a warmer zone, but I think that 2" over the root would work. I'd plant them asap since they have that growth, & cover them if you get a hard frost. They can handle a light frost fine at this stage. Or you can pot them up at the depth you want & plant out later. They are really pretty forgiving. You will love them, I have both of these & they are beautiful.

You can put them out on warm days and bring them in on cold days and nights if you want. They will do better that way and take less hardening off since they have broken dormancy than if you try to grow them by a basement window. A wheelbarrow to easily move them into and out of the garage, or just take the plants out as you head out to work if the temperatures are above freezing. If it's any comfort, after my grandmother died, I divided and brought back a couple Festiva Maxima peony roots from plants that my grandfather had planted many years prior. This was mid-July, and they survived and grew just fine after a couple of days wrapped in damp paper towels. So I imagine that at least some of yours should survive.

Think about it. The digging season in the lower 48 is too late for the growers in Alaska to plant in the ground unless there is an exceptional year. They receive roots that have been kept in cold storage in the spring for planting then. If they can do it you can too. Most of the roots you see in packages have also been kept in cold storage unless they have been shipped from the Southern Hemisphere. The only thing is that the plant growth can be retarded by Spring planting but that will happen if in the ground or in a pot. The reason is that the small roots needed to absorb nutrients are not triggered to grow until the ground is cooler. Being planted close to the surface there may also be some thing about the daylight be coming shorter that can also cue the plants. Planting in pots and waiting until fall is up to you but I would recommend placing those pots in the ground rather than exposing them to the heat of the air surrounding the pots. If you do get them established you may have a problem with some of the nematodes eating from their roots as they are more prevalent in certain types of soil. Your soil may also be too alkali for good growth but in that case I do suggest a raised bed. There are some peonies whose ancestors come from alkali areas of the world. Next year the American Peony Society is planned to have their annual meeting in Oregon again. There will be people there that have much more knowledge of the geographic areas that peonies are from than I am. If he is able to come I would suggest finding Don Hollingworth and asking him about the topic. He is either in his late 80's or may be 90 this year. Kind man and loves to answer questions.