ROB, Sam2 correctly debunked your “proof” that according to the Shulchan Aruch it would be muttar to listen to music during sefirah.
If we’re left only with minhag, then clearly the minhag is to asser during sefirah.
You can’t have it both ways – to matir during the year based on minhag, yet reject the minhag to asser during sefirah.
R’ Moshe in O.C. 1, 166 clearly assers instrumental music during sefirah even according to the opinion that it’s muttar during the year.