I am a French National and currently working in the US under a J1 visa. This visa will expire in May 30. I intend to leave the US to travel to central America and Mexico, then to reenter the country on June 28 to take my baggage and leave the US on June 30. I know this is a risky situation, as I am not supposed to leave and then reenter the US during my 30 days grace period after the J1 expires.
My question is: would an ESTA solve my case at immigration? Can I apply for an ESTA being in possession of a J1 visa? (It is specified on the ESTA website that you can apply for a new authorization if, "You are currently not in possession of a visitor's visa.") Thank you!