Almost your entire list is second, third hand information. Who wrote the book you’re citing, and what were his sources?
Just for one example, no talmidim of rav Moshe say he viewed the state positively. Many have told me that he didn’t address it because he needed his psakim to be accepted by everyone, and most Jews at the time were pro zionist.
Rav henkin wrote in his seforim that the state violated the 3 shavuos. He was very strong in his opposition. How would he then say that saying halel is valid? We don’t praise Hashem for a violation of his will.
Shabtai rappaport married a granddaughter of rav Moshe. He is not a grandson himself. He married a tendler(surprised?), teaches at bar ilan, and has a name that the Torah community accepted on itself not to use since shabsai tzvi. Shabti/shabsi took its place. His testimony is no different than those who say that rav Moshe had a seudah on 5 iyyar… When it was just his lunch(heard from a talmid)