DaMoshe:
Rabbeinu Tam did not break with Rashi’s mesorah, regardless of halachic differences.
Regarding Rabbi JB Soloveichik, I have already written about this, and you are misrepresenting the facts: specifically, that Rabbi JBS did not remain a member of the Moetzes and instead switched to Mizrachi.
As well, his positions were certainly not held in high regard by other gedolim, and some of those gedolim went further than that: for example, Rav Aharon Kotler.
Either way, Rabbi JB Soloveichik himself admitted that he broke with his mesorah.
If you want to rely on your Rabbi, as I said, that’s your business, but this does not create a legitimate mesorah for “Religious Zionism”.
There is no legitimate mesorah for “Religious Zionism”.