re: #9 Alouette
I can absolutely guarantee that if Hanukkah did not occur at the same time of year as a major Christian holiday, it would be totally ignored by the vast majority of American Jews. How many non-Orthodox Jews observe Shavuot, or even know what it is? And it is a much more significant holiday than Hanukkah.
In Renaissance Venice, Purim was the festival most Gentiles knew about, because it coincided with Carnivale.
In India, Shavuos.