It's advisable first to get J-1 extension and then to start the waiver process. I have not found the exact law that says NO to extensions during/after waiver. However, I have observed that sponsoring offices usually refuse to extend J-1 after the waiver is granted and often even during the waiver process if they come to know that waiver procedure is underway. Even if the applicant might not upfront inform the sponsor about waiver process, they still have good chances to know about it because the DoS very often asks the sponsor to provide a "no objection" for granting waiver to the applicant; and sometimes even to get clarifications over the nature of funding provided to the applicant.
Best wishes,
Jigesh
Disclaimer: Personal non-legal point of view only.
