Our intersectionals die completely to ground every winter, just like
herbaceous.

My established Itoh Peonies (Bartzella, Singing in the rain, Morning Lilac) have up to 1' woody stems that do not die.
Newer plants (second year in the ground; Cora Loise and Hillary) have smaller above ground parts. The plants are smaller themselves, so I expect the same result from them in a year or two.

Intersectionals are sterile: no seeds.

I just got some also. They are showing new eyes. Should I plant them just below the soil like a garden peony?

The large, established suppliers of Itoh peonies dig up and sell them in the fall. Early fall is definitely the best time to plant an intersectional. This allows the plant to develop feeder roots before the spring. The lack of feeder roots in bare root plants planted in the spring will result in severe stress on the plant. If it were me, I would plant a bare root Itoh in a large container, keep the container in shade and then take the plant out of the container and plant it in the ground in the fall.

Itoh peonies should be planted with the eyes 1 1/2 to 2 inches below the surface.

Thanks. I've find the peony wholesalers here sell out in the spring.

In my experience the intersectionals settle and grow extremely fast. I would plant it in the ground and make sure it has enough water in the spring. Then I think it would thrive. I grow only tiny roots in containers; in my experience peonies do not like them.

The intersectionals really are wonderful. So full of life!

You really should trade roots, folks, they grow so fast and they are so expensive! (I would share but live in Scandinavia)

The 2 smaller itoh peonies I got this spring looked like herbeceous ones and produce shoots that start out looking herbeceous, but their leaves ultimately have the shape of the tree peonies.

I just got in the mail a bartzella itoh peony and this one looked exactly like a tree peony with all sprouts coming from above ground buds. I guess there might be a range in how close itohs are to each phenotype.

Here are the pictures to show exactly what I mean.

Here is a link that might be useful: Bartzella Itoh peony

My most resent reading indicates Itoh peonies tend to have a very woody root system. Folks have been forced to use a saw to divide them and some question about long term health. Any opinions/experience?