Just like many things in Immigration the rules have changed. While the requirements have been vague to say the least the state department used to allow IAP-66 (J-1 Visas) for pilots that did not have a professional license which was interpreted as anything less then a CPL.
Recently that has changed to PPL with 50 hrs that means in essence that if you have more then this you would not be eligible for the Visa(US Consulates determines elegebility). Having said this, the state department has not exactly done a good job of telling schools / consulates about these changes and things are falling through the cracks. Many schools may not even be aware of this change so you would be best advised to speak to them directly. Make sure that if there is a fee for J-1 visa processing etc. you could get a refund if your application gets denied by the Consulate but other then that it should be worth a try. If the consulate accepts your application (after you answer all questions truthfully) you are in the clear.
It will take a few years for things to get back in aviation and legally working as a CFI would be a good base for your aviation career.