If R’ Moshe said it’s not allowed, is that not enough for you? R’ Moshe zt”l wasn’t just “any Rav”, and he said you shouldn’t listen to music during sefirah.
Personally, I don’t. However, there is disagreement among rabbonim as to what constitutes music. Many hold that it is only LIVE music that is to be avoided. So a sefira tape would be ok, according to that opinion.