I am a French national and currently working in the US under a J-1 visa. This visa will expire on May 30. I intend to leave the US to travel to Central America and Mexico, then to re-enter 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 re-enter the US during my 30-day grace period after the J-1 expires.
Would an ESTA solve my case at Immigration?
Can I apply for an ESTA being in possession of a J-1 visa and then re-enter using the Visa Waiver Program?
(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.")