Yeah, the gen in progenitor is from the same root as genitals but...its also found in a host of words about birth, beginnings, belong to by birth, and eventual being related to, such as:

genesis
generate
genus
germ
gender
gentile

there are specis of lizzard that reproduce by virtual cloning (paragenesis) but since were talking about a new process perhaps what is needed is a new term for the Host and clone(s).