As someone who has been in your position, I would apply for a J1 with a fixed wing school and do your fixed wing commercial. (added expense but you never know, it may come in handy one day - like if you ever decide you want to make money flying)
Then go to a school that has both Helicopters and Airplanes, do your fixed wing CFI, talk them into hiring you as a Airplane CFI - then spend all your time teaching Helicopters!
As long as they hire you as a FW CFI on paper, once you're there it doesn't matter what you do. An expensive option for the visa, but your options are somewhat limited.