Regarding oft misquoted Rav Moshe.
“Rav Moshe’s Ruling
However, this is not so clear-cut nor unanimous. In fact, and although widely and seemingly erroneously quoted as holding that one may indeed switch between ‘First’ and ‘Second Sefirahs’ in different years[18], Rav Moshe Feinstein zt”l, actually qualified such action[19]. He clarifies that for Ashkenazim to be allowed to do so would depend on the difference of opinions between the Bach and Vilna Gaon as to the interpretation of the Rema’s ‘First Sefirah’. He explains that according to the Bach both minhagim are based on keeping 33 days; it technically should not matter which 33 days are kept. Accordingly, one may switch ‘Sefirahs’ in different years.
Yet, according to the Gr”a, the ‘First Sefirah’ is solely due to the Talmidim dying only then. If so, maintains Rav Moshe, how can one switch ‘Sefirahs’, if each is mutually exclusive, based on different accountings? If one holds that the Talmidim only died up until Lag B’Omer, how can he, in the very next year, follow a different minhag, which is based on a shittah that they did not actually die at that time, or vice versa? Therefore, he maintains that according to the Gr”a one may not switch ‘Sefirahs’ from year to year.
Additionally, Rav Moshe holds that the ‘Second Sefirah’ is the true Ashkenazic minhag and that ‘First Sefirah’ is essentially a Sefardic minhag[20]. He therefore concludes that an Ashkenazi may not switch from ‘Second Sefirah’ to the ‘First Sefirah’, as lechatchilla we should not be lenient against the shitta of the Gr”a, except under extremely extenuating circumstances’[21].”