John Becker, welcome to the SCF US classics forum. I hope you enjoy your stay, challenges and/or disagreements notwithstanding. Allow me to add two things to this discussion, which for the most part is out of my range.
1. Let us not forget the footnote in Scott just ahead of #752 which says that in 1940 the USPOD offered to gum full sheets of the imperf reprints for collectors submitting them for that service. Once the stamps were so gummed, what was to stop a collector from having them privately perforated to his or her specifications? John is reminding us that Pat Herst relates that such private perfing was done. Since it is highly probable that the gauge of the private perfs was not the same as regular government issues, side by side comparison should show a mismatch even though the gauge was internally consistent on a particular stamp. If all this be so, what was to stop a private contractor from perfing on the cut lines printed between the panes?
2. To discriminate privately perfed reprints from "reperfed" government issue straight edges it is not sufficient merely to compare the perfs on a cut line with another stamp alone. Those perfs need to be compared with top/bottom and left/right perfs on the stamp itself for internal consistency. For this the perf test developed by Ken Srail becomes invaluable.
John, you will do well to familiarize yourself with the Srail test if you have not already done so. Here is a link to a thread in SCF that applies the test, among other things, and has comment and caveats from Ken Srail himself on its use.
https://goscf.com/t/39330If that doesn't help you can search this forum on "srail test" and get exposed to it that way. Once you know how to do internal comparisons of the stamps in question you can discriminate privately perfed reprints from reperfed government issues.
My suggestion here is based on the understanding that if the perfs on the straight edge do not match up with the perfs on the other three sides, but that most of those other perfs do match up with a known gov't issue, then the stamp was reperforated. But if the perfs on all four sides match up then it was privately perfed. That said, if there were privately perfed sheets that gauged the same as the perfs the USPOD was using, then I don't know how you would distinguish them. Similarly, you cannot readily apply this test to a stamp with compound private perfs if such a thing exists.