No.

Most of the work of Pincus that involved these sort of iterated constructions, where one "pushes the counterexamples out" has never been reworked into modern terms.

In my Ph.D. one of the reasons to develop the notion of an iteration of symmetric extensions was to help and simplify these proofs (also the works of Gershon Sageev). If you look closely, you will see that this is not just presented in the "old method of forcing", but it is also from an era where the distinction between generic and symmetric extension wasn't fully explained in texts (indeed, you can find even papers from the early '80s that refer to what is clearly a symmetric extension as a "generic extension").

Unfortunately, so far, nobody has wanted to take on this mantle, and I have a lot on my hands as it is. I am happy to collaborate or give advice, if anyone wants to go for it.