Thank you Gary and Nick. I found an article by American Peony Society that makes the same distinction between itoh and intersectional, (i.e. a woody crossed with lactiflora vs another herbaceous). But it also says there are very few examples of intersectional peonies, so I can see how they might be lumped together with either name applied.
I must be using the term "hybrid" incorrectly. To me that means any cross between two different species, but in the peony world it apparently refers to crosses of only herbaceous peonies. Thanks for the explanation.
Since the buds might survive the winter, maybe I'll just remove the leafy portion and leave the stems--although the stems are not very woody. Might try the bud propagation some time, too.
