cherrybim: You have brought some background to this matter. R’Moshe zz’l believed that music is ossur all year round (see some of his teshuvos) and only reluctanlty acquiesced to the kulos of today.Hence, R’Moshe zz’l felt that during sefirah we should assert the halacha of all year round. And, if you read the teshuvos on music and sefirah ,it becomes even clearer that R’Moshe zz’l felt thast this was an extension of all year round halacha.
However, as a large part of klal yisroel is “meikel”on music all year round, it becomes much more difficult to prohibit music during sefirah. It seems that the “tsibbur’ accepted an issur for live performances but many groups are “meikel”‘ on recorded music, such as Chabad, mentioned by yourself, Rab Hutner zz’l and his talmidim and even R”moshe zz’l himself who allowed chazanut on sefirah.
This approach would at least give the Issur of music during sefirah some substance, which it doesn’t have now.