Jimbo,
ALL-ATPS does NOT issue any visas to foreign students. I know this because I phoned and asked about it. No J-1, M-1, or F-1 visas. The only students they take are US citizens or Green Card holders (permanent residency). Sorry to be the bearer of bad news but it is true. The same goes for RAA (Regional Airline Academy). FlightSafety Academy however will issue you an M-1 to do your ratings but only issue the J-1 if you have done no more than a PPL and wish to complete the rest at FlightSafety. You do the flight training for like a year and then work for a year. If you've already got your CPL-ME-IFR then they will not issue you the J-1. Perhaps you could try Embry-Riddle Aeronautical University and enrol in a degree program on an F-1 visa and work on your CFIs as well.
Good luck.
TL