Sorry I am not really up to all the philosophical debate here. But one thing is in my purview and that is pshat in a gemara.
R’ Yehoshua was saying that Rabban Gamliel made the incorrect psak. He was told by R Akiva, and subsequently even more clearly by R’ Dosa ben Harkinas, that Kiddush Hachodesh is dependent on the Nasi, and even if he’s wrong, he’s still right, because the entire power of kiddush hachodesh is invested in Klal Yisroel in general, and specifically the Nasi. The gemara says that the Malachim sit around waiting for Klal Yisroel to be mekadesh Chodesh Tishrei before they sit down to Din. To paraphrase the old sign, “Rule #1, the boss is always be right, Rule #2, if the boss is wrong, see rule #1.”
So we don’t say that R Yehoshua was right. Only that if Rabban Gamliel would have used his intuition better, as R Yehoshua would have and his intiution was correct, he would have rejected those eidim and paskened differently, delaying ROsh Hashana and Yom Kippur by a day. But since he didn’t, R Yehoshua is WRONG, and Rabban Gamliel is correct. The halachic principles aren’t telling us to follow Rabban Gamliel even if he’s wrong. The halachic principles are telling us that Rabban Gamliel is right.