The difference between these opinions lays the groundwork for establishing the answer. Rabbi Elazar’s opinion is not really accepted, so we confine the remainder of our answer to the 7th of Adar opinions.

There is a debate between Rabbi Yosef Karo and Rabbi Moshe Isserles in the Shulchan Arukh 568:7 as to observing a yartzeit during the leap year, in the event that the death took place during a regular year.

Rabbi Karo believes it should take place in Adar II, while Rabbi Isserles calls for it to be observed in Adar I in order to observe the day as soon as possible. He also notes the practice that some observe the yartzeit in both Adars.

While others argue that when a birthday or yartzeit takes place in a leap year, the proper date to observe the event in a different leap year is the exact date – an Adar I date in Adar I, and an Adar II date in Adar II (Mishneh Brurah 55:43).

The Magen Avraham disagrees with this idea, arguing that one ought to count year by year, instead of paying attention to a leap-year birth date. It is his opinion that all bar mitzvah birthdays, for example, will only be observed in Adar II, regardless of whether one was born in Adar I.

Rabbi Jacob Emden was asked this very same question regarding Moshe’s yartzeit in Adar I or Adar II (She’eilat Yaabetz 1:117), and he explained that it all depends on how one views Moshe’s yartzeit.

Haman rejoiced that his lottery fell in Adar because he knew of Moshe’s death in Adar and felt it was a bad month for the Jews. As such, the miracle of Purim is inextricably linked to the yartzeit of Moshe. With this logic, the month in which we observe Purim is the month when Moshe’s yartzeit should be observed.

In the final analysis, the jury is still out on the exact month of Moshe’s death – Adar I of a leap year, or Adar of a regular year.

Those who want to follow the practice of the Shulchan Arukh (580:2) to fast are encouraged to do so. If you want to fast twice, like the Rema suggests in 568:7, kudos to you.

But if you’re looking to get out of tachanun twice, I’m pretty sure that’s not what Rabbi Isserles was suggesting.