Coming from a hard science background I’m always a little suspicious of social science research (too small sample sizes and too many variables!)
But if you’re looking for some research on how songs help with teaching languages, this little research paper might be useful.
Songs as an aid for language acquisition by Daniele Schöna
I know that school directors especially, are always looking for data and research to support new ideas. Hope it helps!
P.S. Do also check out the research done on Genki English specifically too!