This last link was excellent, and I browsed Peter Klein’s name on mises.org, and this presentation of his helped a lot:
in particular, the last slide of the presentation entitled “Hayek on Mises”.
To me it seems striking that Hayek writes about this in 1981, 60 years after Mises’s Socialism, and only then saying only that it “now seems to him”… that Mises was factually wrong. So it took him quite a while to settle on a particular interpretation of Mises’s words. That tells me how subtle the differences between the two of them were. I’d think that whoever is trying to dehomogenize them has a seriously complex problem at hand, and so the critical audience should not accept anything but a very high quality analysis.