I’m not a Brisker but we should do a test.
Find out if Briskers would go to Rav Shlomo Zalman for shailas and find out if they would go to R’ Kook for one. My kollel is near geula so it shouldn’t be hard for me to find one.
The difference in my opinion is that Heter Mechira is like opening bottles on Shabbos (also R Shlomo Zalman’s heter)- a big kula but not a radical departure from Halacha. Zionism though, it didn’t start by the frum. We always had a ahava for E”Y but Zionism was a modern creation and you know how some of us feel about that. V’haMaskil Yavin.
Also, what did Reish Lakish ever do to you that he lost his chezkos ne’emanos by you?