I've been checking around for you about your problem. Here's a response I got from a guy in Germany (that's why the post reads kind of strange). I asked him if these will sprout from dormant eyes if the main stem is chomped.

Hi, yes they have! After blooming ( from top of the stem, which is built as a tuber ) a dormant eye ( you have litterally translated the same word as we have! ) or more start for the foliage. I have seen pictures on the web of Indian farmers cutting big paeonis in "little" pieces of one pound to till their field ( hope I found the right expression in my dictionary! ) I.e. make the pieces grow for the next harvest.
Seeems crude to ( for? ) us, but that's lfe!
Bye
hermann