Rav Moshe permitted any type of music in spite of the ban after the Churban since we need it in today’s times because of our nervousness, like a r’fuah. Perhaps the same heter applies for s’fira.
Do you have a source for that?
In ??”? ?’ ??”?, he is ????? on instrumental music during the year, and writes that even according to the ??????, it’s ???? during ?????.