Square; you bring up several points that are important to discuss.
1. You’re mechaven almost verbatim to the position of Rav Yosef Albo in ikkarim who disagrees with the rambam regarding bias hamoshiach’s ikkar status based on your logic. He says that something that is a machlokes(even one against hundreds) cannot be considered an ikkar of our emunah. The fact that the gemara itself not only is docheh rav hilel, but says uncharacteristically “shara lei marei”, that his (rav hillel’s) master should forgive him for saying such a thing. So maskanas hagemara is that rav hilel isn’t just a minority view, it’s an intrinsically wrong position. That being said, how can we call it an ikkar if an amora didn’t hold of it?
Achronim give answers to this kasha of Rav Albo. One answer I saw years ago is that an undisputed ikkar is that nevuas moshe rabbeinu was bigger than any other navi before or after him. Rav Albo would seem to agree with this (he doesn’t question it, as far as I remember). Wheb Miriam took issue with Moshe distancing himself from Yocheved, her cheshbon was that other neviim had not been commanded to do so, and that she felt this was an error. Miriam it seems, did not at that point accept that Moshe was greater than all the other neviim (including herself), and that she can disagree with him. When she was shown that she was mistaken, that ikkar was established. Torah doesn’t exist in a vacuum; halacha expands and takes the form of the decisions of those imbued with such authority; tanaim, amoraim, rishonim and achronim. What was a possibility in the time of Miriam was not possible in the times of rav hillel, and what was possible in the times of rav hillel is not possible in the times of the rambam. Rav elyashiv’s statement regarding rabbeinu avrohom ben horambam’s opinions of chazal/science applies here as well “he was able to say it, we cannot”.
2. There isn’t just one source for what your rebbeim told you. It’s all over rishonim like the kuzari, rabbeinu yona, and tons of achronim, ranging from rav hirsch, the gr”a, chazon ish, ramchal…you can find a long list in the perush on the chovos halevavos called “lev tov”, printed in many standard editions of that sefer. In the hakdama to shaar hayichud he goes through it.
3. Emunah based on mesorah isn’t childish; it’s the acknowledgment of jewish history being filled with divinity and awareness of Hashem. It’s the understanding that our nation stood by har sinai, and that its authenticity shouldn’t be any more suspect than the American revolution. Havchana, seeing Hashem in creation and history, isn’t derishah vechakirah; it’s advocated by basically everyone.