Space Worm from
The Empire Strikes Back - Yes (plus non Toho bonus points)
Giant Squid/Octopus from
It Came From Beneath The Sea - Yes (plus non Toho bonus points)
The Monster from
Cloverfield - an intentionally vague Yes (plus non Toho bonus points)
The energy ball throwing bugs from the
Starship Troopers film - No, not big enough.
Galactus - the comics version, not the stupid film thing - This one is tough to decide on. While Galactus could change his size at will he really is not so much a monster as a universal force of balance. Plus the fact the he was usually depicted as being large but not as large as the monsters set by the criteria. Going to have to go with a No on this one.
Most of the larger creatures of the Cthulhu mythos especially Cthulhu, avatars of Yog-Sothoth, etc. - borderline SF since they were apparently alien, not demonic as such - Yes, Alien vs. Demonic does not matter as it was not part of the original criteria. (plus non Toho bonus points)
The Stay-Puft Marshmallow Man from the first Ghostbusters film if you accept that as SF rather than supernatural - No, while big still not big enough.
Lexx and Moya, if living starships count. Lexx ate planets occasionally, so is definitely a monster. Yes on Lexx after doing some due diligence research. No on Moya as she really never did anything overtly monstrous.
That gives the win to ffutures for the right to post the next challenge.
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Just to give some examples of what was in my head when this question was posted.
Rodan
Mothra
Ghidorah
Gamera
Reptilicus
Gorgo
As for the final question in my original post a mistake was made on my part. The original Godzilla was released in 1954 while the film referred to was released in 1957. Somehow it got into my head that the original Godzilla was released in 1958.
That 1957 film was:
Kronos.
It remains one of the few American movies in this genre albeit one with a more Sci-Fi bend to it than its Japanese counterparts.