I know you become ineligible for the J1 if you have more than an FAA Private or more than 50 hours experience. That rule could also incorporate any ICAO Private, although I don't know for sure. Just don't tell them when you're applying for the Visa. After you get it than you can then proceed to get your FAA ratings while using your aeronautical experience to meet the FAR requirements. I've never heard of immigration checking up on your aeronautical experience while you're in your course, although I could be wrong.
Just be careful about the little lies you tell so that you don't get caught out by them!! This angle probably won't go down very well with some of the Americans on here, but if your future career depends on it, you gotta do what you gotta do!!