This is very cool! Superb list, by the way.
Personally, I'd say that most of the time Godzilla is Chaotic Good/Neutral, with some exceptions. Shin, GMK and 1954 I'd say are Chaotic Evil for sure, because they were actually trying to destroy as much as they could and went out of their way to do so.
I did something similar a while back. It doesn't have all the monsters, because I only used the ones I felt like worked best with each alignment:
