It may come as a shock to some, but Rav Kook was vehemently against anyone changing their pronunciation. Rav Kook acutely felt that the issue of 12 gates/approaches to the Beis Hamikdosh, despite the concept of Shaar Hakolell (the 13th gate for those who knew not what their tradition was, and which the Ari felt was his Nusach, and which the B’aal HaTanya refined) was Kodesh Kodoshim.
If your father/grandfather pronounced things a certain way and/or followed a certain Nusach, Rav Kook was implacably against the Ben Yehuda approach of creating a universal style new pronunciation. This is known by anyone who spoke with Rav Kook.
Rav Kook preferred to speak in Loshon Kodesh. That’s another matter. I feel though that people need to understand that this icon of Jewish Rabbinic History was far less malleable despite his extreme and burning Ahavas Yisrael and Ahavas HaTorah and Eretz HaKodesh than people realise.
Certainly Poskim including Reb Moshe and the Minchas Elozor were authoritative in their machlokes and rulings on this matter, but it’s interesting to note Rav Kook’s view.
At Elwood Shule, I remember as a boy asking the older men (in Yiddish) what did your father say in Musaf, “Kesser or Nakdishach”. Invariably they said “Kesser” but once they moved to anglicised Melbourne, they simply went along with the English influenced Nusach of the regal Rabbinate. My father ע’’ה told me that he always said “Kesser” and a few times, I heard him mumble “Brich Hu L’Aylo Mikol Birchso Veshiroso” as opposed to Amen or Brich Hu. I keep this, and cherish the unadulterated Minhag Avoseynu.