I'm sorry if I bring you down but;
Strictly speaking you cannot apply for a J-1, because as said before you already have a CPL. If you want to and another class (fixed wing) that doesn't matter because you are a commercial pilot.
However it's up to the school to decide, I know of schools that still get you the J-1. The only thing you can do is talk to the schools.
It's not possible to apply for a H visa yourself. You have to be sponsored ie. you employer has to apply. The chances of getting a H visa as a pilot are very slim. The employer has to prove that he can't find a qualified American. So unless you have some very particular qualifications you'll have a problem.
If you fly say EMS and you have more than 2500 hours, multi exp. ex. mil. You might have a chance in EMS in remote areas. The same goes for Alaska, it's easier there, but you need to be (over) qualified.