Well, I do basically agree with you that the vast majority of II's did get the Firestones or the Goodyears. But, I'm certain that I've seen factory photos of the RWL Generals as well. I'll have to look and see if I can find one.
Regardless, the listing of the other tire manufacturers appears in several charts within a looseleaf pamphlet I have, (possibly a reprint) titled Mustang II 1976 Specifications Guide, which is also states on its cover: Specifications Unit, District Operations Section, Distribution Dept-FDGO April 30, 1975.
There are numerous charts in it, that show availability of standard and some optional items, along with the corresponding ordering codes the dealers were to use. While it may not be proof positve about this matter, it certainly points to the distinct possibility that old Henry didn't put all his eggs in one basket.