I don't believe it that a hunter gatherer could be turned into a farmer.
Most HG were reluctant, that's true, but it happened often enough and don't forget, even the first farmers were foragers before, like the Natufians.
Besides, hunter gatherers lived in small groups and their density had never been high.
Those foragers were eliminated for the most part, with only single individuals surviving here and there. But the situation was different in the places mentioned, among e.g. Mesolithic communities in Scandinavia and Southern Russia. There people transitioned to a more sedentary, higher culture without turning into full farmers, but became pastoralists only later.
It is a very different way of life from farmers. Now you describe a situation "HG taking farmer wives" it is not working, as HG might have lived in matriarchal communities (at least in the Baltics they likely did)
The Baltic foragers were among the losers, can't say much about them, but matriarchy is a myth, the true Bachofen matriarchy never existed and the hunter-fishers in Southern Russia seem to have been patriarchal, so were other groups. The pattern of patriarchal clans eliminating each other, but accepting some foreign wives of the defeated party is old, its older than farming.
So do you think hunter gatherers who lived freely wanted to become farmers?
Usually not, but under specific circumstances yes, especially if becoming integrated into larger Neolithic frameworks with new symbols, ideologies and opportunities.
I cannot see how to turn a hunter gatherer into farmer. Neither a man or a woman.
Early farming was often enough largely a female business. Hoe-farming in particular is a typical female occupation. So what I would imagine happened somewhere in Northern Italy-Southern France, if following the study, is that the local hunter gatherers took, one way or another, farmer wives from the Cardial Neolithic people. Those women, this is something you see quite often, kept a lot of their ways from home and were actually quite useful for the clan, as they added resources and knowledge. So it might have happened not in one, but in a couple of generations, with the mixed offspring becoming more and more like the Cardial people, but not fully so and, probably because of a different language, ethnicity and ideology, they didn't intermix afterwards with other Cardial, after the initial mixture, at least there were not foreign males accepted. In the earliest farming communities, you often see males as hunters and pastoralists, while the females did gathering and hoe-farming. Basically the females could feed themselves for the most part, which made them much more valuable than forager wives which could contribute less and needed more investment. That's not to say it was like that everywhere, again those foragers living from aquatic foods were different, but its true for many typical hunters with gathering being of lower importance.
A lot of hoe-farming societies are polygynic for that reason too, because women produce more than they consume. Primary hunters with a low importance of farming, high investment of males into their wives, are less likely to be polygynic in comparison. I think farmer wives were, not just because they were prettier, quite in demand once foragers saw how it worked out. Most of the pottery was a female business too. So basically you have to look at the male side of things for differences in such a mixed community, and there you can see it in Southern France: They were Cardial Neolithics, but deviated in a typical way. Because the female contribution was Cardial, the male was not.
