charlie:
I did not know which day the Orthodox Christmas was, but my analysis is correct. The reason some celebrate nittel on Jan 6 or whenever is to accord with the Orthodox Christmas.
You are correct that since 1900 that has been Jan 7, and in 2100 it will be Jan 8. (At which time we will begin saying tal umatar on Dec 5/6 since we also use the equivalent of the Julian calendar for tal umatar, birchas hachama, and maybe some other stuff.)
I feel like we can have a better relationship on this forum. I’ll try to be nicer in the future.