Hi -- I don't know if I can help out much. In Wagners the 'F' designation was typically used where the '9' was used in the Griswold, & sometimes both together. The 'P' is a completely different pan with trapazoidal cups(like the 'N'), which so far has only(to my knowledge) been seen in aluminum.
So I think it is more likely that the 'p' marking is either a misformed 'f'. or a marking specific to some other company, or even a 'quality control' mark -- tho believe that the 'f' is more likely.
My own prejudice is that Griswold may, in fact, have initially produced early, otherwise unmarked Wagner #9/'F' style pans with the double loop handles. We generally don't credit these to Gris as there is no PNs on them(but the early molds generally didn't have PNs), & what we know is Gris has the straight(vs. double loop) end tabs.
The quality of these is often excellent, but most of the early major companies also produced high quality -- so it's hard to differentiate on that basis.
But like many pieces in what I call 'the common era' period, I think that there is a good chance that these were made by Gris for Wagner, when Wagner was just getting started, but wanted to present a complete product line, but wasn't up to all of its own production. Perhaps, as a slight support, the 'missing' #19, 6-cup golfball pan that so far only appears in the Gris. catalogs, also has a loop handle.
'Net botttom' -- if the 12 'golfball' has something that looks like an 'f' it should probably be considered Wagner, even if produced by Gris.
Wish I remembered better about the 'gate marks' -- joel schiff