A visa is quite expensive for the school, too. No one will give you a visa if you have just your FAA CFI(H) left to do.
My recommendation would be to look for a combined RW/FW training school and talk to them if you could join their course with an F1-visa (the replacement for the good old J1). Then go through their FW-program and do your CFI (H) in addition to that. After finishing up you are eligible to work in the states for 12 months (but you have to find a job within 60 days after finishing your training if I remember correctly).
You could also look for a degree program in aviation which allows you finish your CFI(H) and work on an F1 visa. There are options and loop holes and I know people who have done it (not me) but it takes some investigation and talking to the schools and colleges. I'm pretty sure though that you have to come up with a different reason than "I wanna work in the US" to make it work, i.e. "I found out that I totally love FW and want to do my addon and CFI! And CFI(H) on the side..."
M1 is def. not an option and is only valid for as long as your training takes.
Just out of curiousity: what took you 24 months to complete your CPL(H)?
