The reason that the Satmar Rebbe and the Litvishe Gedolim are accepted universally as Gedolim including by the Mizrachi, is simply because they are indisputably Gedolim. The Mizrachi has not produced anyone of the caliber of the Satmar Rebbe, Rav Shach, Rav Elchonan, Rav Elyashev, etc.
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No Zalmen, it’s just that closed minded people refuse to recognize as great anyone who operates outside the small box of what you terms legitimate. For you it’s axiomatic. It is not torah scholarship or actual yirat Shamayim that matters. Rather it’s doctine and the chitzyoinius of dress etc that matter. Answer this question please. Was R. Esriel Hildesheimer a gadol in your eyes? How about the Sridei Eish?
On a differnet note, do you recall how the Satmer Rav left Hungary in 1944?