I know people who where denied a J-1 visa, when they tried to follow this route.
The school applying for an H-3 (B) visa is BS. If you'd do your training up to CFI on an M-1, you don't have work experience and for an H visa they need to prove they can't find any suitable US citizen.
These promises are made a lot but after the school made it's money, it's just "Sorry"
The only way to go is the right way, either HAI or Hillsboro on a J-1 giving you 24 months to get it done. Shortcuts aren't worth the trouble and risk.