My DD has quick turnaround time from remedial, about one month, but slightly longer wait for medical waiver, about three months - her approval came one week before she left for freshman year. As you can see from the answers, response times can vary widely. Best wishes.
I think it must depend on the remedial. My DS had a remedial which only required him to answer questions on a form, sign and date it and send it in to DoDMERB. He scanned the document and emailed it to them and a day or two later he was notified that he was qualified.
DD had one specialist appointment, personal statement, and medical records to submit. The process took 3 months to receive waivers. Be prompt with requests. Patience is a must; the process takes time. Good luck!