So, Anki did help me learn a few of them, while a few would just never stick for some reason. Amusingly, the few birthdays I did learn didn't really help me because even though I knew the birthdays, they wouldn't come to mind until days or weeks after the birthday passed!

So what I'd actually need is "what are all the birthdays that occur this month", and then have a ritual habit installed that at the first day of the month I would spend a few minutes pondering this list in my mind.

(Again, the birthday wall calendar would probably work better here...)