Your points are well articulated, and I see where you are coming from. A few points:
I see the creation of MechaGodzilla himself as a fantasy element. It's totally ridiculous on the face of it. Right from the start, I jettison any expectation that this will be a "realistic" film.
I actually don't mind the psychic stuff later on in the series, particularly in MechaGodzilla, where the goofiness of the concept works much better IMO. It's when contrasted with the somewhat believable science of *parts* of Biollante I rebel
Of course, one has to accept the existence of Godzilla from the start, and they do at least have the characters deal with and grapple with the very fact of his existence. In the case of the two SuperX craft, think about the research, time and radical new science that would have to go into building such a craft. Try to imagine a realistic film like Close Encounters suddenly having the SuperX show up at the end to deal with the mothership. It would be jarring, to say the least, and probably laughed off the screen. It is in this type of science fiction construct that I find the SuperX craft embarrassing. They just kind of "show up."
Personally, I like the G '85 score EXCEPT the SuperX march. I saw the film during the initial theatrical release on two different occasions, and both times there were lots of bad laughs from the audience when the ship showed up. One of them was mine.
The only hand wringing I see is really in movies like Godzilla vs. Mothra or Godzilla vs. Destroyah where it feels like the characters are really trying to convince me that what they think are super important issues are super important.
TOTALLY AGREED. I am thankful that you see exactly what I am talking about in regard to this element of the Heisei series. Obviously I see this in Biollante too where you do not. I also totally agree with this statement:
The Godzilla films, especially the heisei stuff, really ride the line between fantasy and scifi
Some of this is personal preference, but I would prefer that they either go one way or the other. And it is also my personal preference that if they go the fantasy route they keep it light and entertaining rather than serious, heavy, and pretentious. This is why I tend to prefer the Showa series as a whole. Sekizawa wisely concentrated on keeping the films light and character driven once the heavy themes of the original Gojira had been removed from the series. There are only so many ways you can keep making the point that Godzilla is a symbol of nuclear aggression and a stand-in for the bomb.
One statement of yours I totally disagree with:
psychics and telekinesis are ... legit scifi concepts
There is absolutely no science behind either of these concepts - at least as far as human beings here on this planet (beings from Vulcan, on the other hand, may be excepted