Wang Eye
You are correct on the J1 issue as I myself had a J1. However, the US school/Airline needs to be approved to offer the Visa. Bascially, they send you the paperwork, you go to the Embassy and get issued a visa. You cannot have any licences before you apply and the paperwork will state what type of work experience you will be allowed to do whether or not for renumeration. Even though you may not be getting paid for the job ie students paying for their Airline time, this is still considered a job if the aircraft requires 2 pilots. Therefore in the eyes of US Immigration you will need to have a Work Visa to sit in the aircraft and pay for the time. I tried this route myself!
Ambassador are not approved to do this - in fact there seem to be just 4 schools that can in Florida. Not even Flair is J1 approved. You can find all listed schools at the US Embassy website.
As for the licences, to work in the US on a J1 you are supposed to be going to the US to get training and exercise this training. Therefore, the training must be a minimum of FAA Commercial licence.
