[LINK] Steven Pinker on "The false allure of group selection"

What are you trying to argue? Pinker's article says,

Some mathematical models of "group selection" are really just individual selection in the context of groups.[2] The modeler arbitrarily stipulates that the dividend in fitness that accrues to the individual from the fate of the group does not count as "individual fitness."

If you think that "new group selectionists" would agree with this, why call them that? The 'old' kind doesn't seem to have gone away, since you yourself cite articles explicitly arguing against them:

Several recent papers, however, have objected that inclusive fitness theory is unable to deal with strong selection or with non-additive fitness effects, and concluded that the group selection framework is more general, or even that the two are not equivalent after all. Yet, these same problems have already been identified and resolved in the literature.

Another of your cited abstracts gets more specific:

In this paper, we start by addressing Traulsen and Nowak's challenge and demonstrate that all their results can be obtained by an application of kin selection theory. We then extend Traulsen and Nowak's model to life history conditions that have been previously studied. This allows us to highlight the differences and similarities between Traulsen and Nowak's model and typical kin selection models and also to broaden the scope of their results. (emphasis added)

Coyne's anti-group-selection piece quotes an overlapping group of authors as follows:

“No group selection model has ever been constructed where the same result cannot be found with kin selection theory”. “The group selection approach has proved to be less useful than the kin selection approach.” (ditto) “The application of group selection theory has led to much confusion and time wasting.” It is, as the authors say, “easy to misapply, leading to incorrect statements about how natural selection operates,” it is “not distinct from kin selection”, and it “often leads to the confusing redefinition of terms and the use of confusing jargon.”

You also cite people who would at least partly disagree with the bolded part of that. But even they might agree with the last point. They appear to recommend the dual-perspective approach for people who thoroughly understand the individual fitness approach already, and could explain any valid evolutionary argument in those terms.