Also, how long does it typically take for DoDMERB to update your status after completing the physicals and tests? Basically asking how long does it take them to get back to you saying that you're cleared or that you need a waiver?
I think you should be okay. Sometimes service academies will give out conditional appointments, meaning that you get appointed as long as you end up passing your DODMERB exam.
Also, many of the remedials do not require a doctor visit, so double check on that.