Jeff,
Thanks for posting that information and photos. I can see your point that a tapered opening between the claws or maybe an opening with two stages of width would enable the puller to get to the third bite. However, perhaps the claims of the patent were not fully executed in the actual production of the spike. That is common with patents. As far as I know, no Greer spikes have been found that have that rib on the non-rail side as is shown in the patent. Maybe there never was a provision for a third bite.
You mentioned the “F” configuration puller that was used. If I understand it, that would be a puller where the handle extends perpendicular to the rail, whereas the patent claims a puller with a handle that runs parallel to the rail with its fulcrum resting on the rail base. So it appears that the puller mysteries that I asked about may have been obstacles that did not exist because they were circumvented by not following the design of that patent claims. I also suspect that the “F” puller rested its fulcrum on the tie rather than on the rail base, and thus did not deliver the advantages claimed in the patent about using the rail base as support for the puller fulcrum.
If my speculation is all true, it appears that all of the advantages claimed in the patent for this unique spike design never materialized in actual practice because they posed practical problems that Greer failed to foresee. My guess is that the Greer spike ended up being just another ordinary spike with an extra head having no purpose.
It has been mentioned that patents often made unique claims in order to get around the claims of conflicting patents. That is true, but patents also sought to claim new, unique features in order to simply get a patent. It is often the case that these unique features end up having no practical benefit or are impractical to manufacture.