Your comments

Hi! I can. So for instance, I'm transgender and the dates of my Hebrew name change or the beginning of my transition are meaningful events that don't fit under the category of x's Hebrew __________. I could also imagine the date on which a person converts, whether when they dip in the mikvah or their first time getting called to an aliyah, or the date which a person is divorced by a beit din if it's an unhappy marriage, as well as many other significant moments - there are likely many such events which are Judaically meaningful but not a relationship anniversary.  Does that make things more clear? 

In terms of leap months and such yeah I can imagine it would need to be postponed similar to birthdays.