Here's an advert from 1940:
... where we can see that Gillette's New whether it be long slot, twin slot, short pin or biased pin, it would fit all these blades.
Granted, the round pin New (with the lateral tabs) produced about the same time would only have fitted Gillette blades (like the Gillette Blue with the universal cutout) and not in any of these blades due to the diamond shape rather than round shape. Buy a GIllette razor, use Gillette blades.
... and so I return to my thoughts about (a) these bias pin/short pin razors being Service Kit; (b) the plethora of blade shapes and styles. Put them together and
you have a razor with a top cap that has the most minimal amount of pin to accept the widest choice of blade without the pin size/position tripping up over the razor design.
I've PM'd MacDaddy. Thanks
@TobyC