It is true that Zionist-leaning sources sometimes distort things to fit their agenda, but this is also true sometimes with ant-Zionist sources. Many anti-Zionist publications, for example will claim that all Gedolim were against the state, completely ignoring Rav Dessler’s letter (Michtav Meliyahu volume 3, page 352), The Tzitz Eleizer’s Teshuvah, the Ponivitzer Rav’s positive view, as well as the many other Gedolim who viewed it positively. With Rav Kook as well, read any Neturei Karta publication; they pretend Rav Kook was a pariah rejected by all the Gedolim. To pretend that distortion only happens in one direction is just silly and untrue.
About Rav Yoshe Ber, i heard a completely different version of what he said. I heard that he said that he wasn’t impressed by Rav Kook’s scholarship, but he was impressed by his Tzidkus. This changes the whole picture. If it’s in writing though, then i would love to see it inside. where is it written? Also, keep in mind that Rav Yoshe Ber delivered a Shiur titled “Remembering Rav Kook” in which he praises Rav Kook and discusses the great contributions he made to the Jewish world (the Shiur can be found on YUTorah). Rav Herschel Schachter a close Talmid of the Rav often quotes Rav Kook, as well.
It is funny you are accusing Rav Nosson Kamenetsky of not being reliable being that he spent decades painstakingly doing research for “The Making of a Gadol”, making sure his information was accurate. The fact that it was banned has nothing to do with the credibility of the book; it’s because some of the Gedolim felt that some of the stories should not be published because people might interpret them in a bad light. It seems, however, that there were Kanoim who spread lies about the book to some of the Gedolim, including telling them that Rav Nosson continued to distribute the book after they told him not to (listen to “Making of a Ban” by Rav Nosson Kamenetsky (on YUTorah)). Incidentally, Rav Moshe Shternbuch, who you quoted earlier in this thread, thought highly of the book and encouraged people to read it. As did Rav Zelik Epstein ZT”L. The quote can be found in “Making of a Gadol, page 1087).
I am in fact familiar with what Rav Elchonon writes; however he is clear from the language of the letter that he is writing this in only in response to the fact that “It is well known that he [Rav Kook] supports Keren Hayesod”. It is clear, however, that contrary to what many people thought, Rav Kook did not support Keren Hayesod. As such, Rav Elchanan would not have wrote what he wrote.
The Sephardi Beis Din may have put Rav Kook in Cherem; as many Kanooim did, but the views of the Gedolei Hador matter much more. Rav Ovadya Yosef, the leading Sefardi Posek, quotes Rav Kook all the time in his Seforim, giving him honorable titles.
Where does the Steipler write the comment you wrote? Anyway, it’s clear that Ruba Diruba of the Gedolei Yisroel viewed Rav Kook as a Gadol; not necessarily did they agree with his Hashkfah, but they viewed him as a great Gadol. You’re assuming that they would have been Chozer, but i don’t see any reason to say assume that.
About the Lubavicher Rebbe, many Gedolim were Machshiv him, including Rav Avigdor Miller who equated him with the Satmar Rebbe. See this quote
“Look, if you advance beyond that stage, then all Rebbes become “My Rebbe.” All Rebbes! The Satmerer Rebbe! Ahh! Zol ehr lang leiben! He’s a wonderful man. A big warrior; and he accomplished for us so much. The Lubavitcher Rebbe, zol ehr lang leiben! He accomplished so much and he is accomplishing. They should both be our Rebbes” (Toras Avigdor)
What makes you say that they were Chozer?