Nev,
גורל הגר””א is by far just a random flip. Nor can it be done by a simple person, officially you need to have obtained somewhat the level of Ruach haKodesh. I think Rav Tzvi Pesach Frank relied once on Rav Aryeh Levin’s Goral.
In any case, that is precisely the point, they are giving the Rebbes letters the same status as כביכול the word of hashem. I have no Taayne it basically speaks on it’s own. It indicates how far this has taken the Moshiach cult.
Think about it, no one ever suggest using a Zohar or even a Tanya for any of those, this is a new invention.
Anyone that thinks it’s the same as just doing the Goral haGra needs to rethink what the very issue at hand is.