There are three things that are stopping Showa Godzilla from getting in. Three really big ones that make it impossible, from greatest to least.
A. Anthony, Greyshot's boss, nixed it. As he owns the site, his say goes over all. If I do recall correctly, he saw little point.
B. We currently have Godzilla (Heisei), Godzilla (Legendary), Zilla, Godzilla Juinor, and Godzillasaurus in. That's five monsters with the name Godzilla in it that could be considered pure, ignoring SpaceGodzilla and Kiryu respectively for their differences, and Mechagodzilla Showa's many skins. This ties into my third point a bit
C. Showa Godzilla is redundant. Early Showa (55-68) is easily written off with Heisei Godzilla, having similar temperments and all. And with the more heroic side, you already have two options. The first is to use Zilla Jr as your heroic Godzila role leaping around and doing some pretty wild things as he did in the TV series. Your second is to write using Heisei Godzilla as Showa Godzilla, which has been done before almost more than actual Heisei's
character traits. You could even in theory have Legendary be heroic, which wouldn't be too terribly out of character for the restoration of balance. Between these three, what unqiue thing does Showa Godzilla bring besides one special ability?
I can get why you'd want to, but there's no real need to do so. Better to work on another monster to get in rather than another large prehistoric saurian monster that can be interchanged easily. Like the Trilopods, or one of the crazy Marvel monsters. Not gonna lie, I'd write the hell out of a match for the flying saucer looking one. Rhiahn would be fun to add, have strange abilities, and be unique enough to stick out from the other monsters. I'd argue moreso than Showa Godzilla.