Check out this website. She said that she was able to propagate her Bartzella Itoh 4 different ways:

http://www.southernpeony.com/2013/05/2013-peony-experiments-intersectional.html

Thanks...it certainly seems like these peonies are robust. But those all seem to be divisions and I am specifically seeking to propagate a clone of a single flowering stem. I suppose I could follow it down to the base and seek to divide it off but the more precise route (or should I say root? :)) would be to snip it, dip it (in hormone) and root it. Has anybody done this?

I think that you miss her last two ways. She said she was able to grow new plants from cuttings of new wood(1 year old) as well as old wood (older than 1 year). I think she just put the cuttings in the soil and the cuttings grow roots on their own. But if you want to add rooting hormone to the stems, I am sure you will probably get faster results. I have read that you can also propagate by sticking pruned stems into the soil in the fall and they will grow into plants by spring although the success rate is about 50%.

The key to getting them too take is to have very good draining soil, and to make sure the spring rains don't make the soil too wet, but overall, any piece with an eye usually takes root for me whenever I try to propagate itoh peonies.

These little cuttings have transformed into large flowering plants this year.

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

OK, thanks. It will be fun if I can get a whole plant of these flowers.