The school has specific criteria for adding homeschool classes to the transcript with an S grade. I wonder if he can do Phys Ed as homeschooled in the summer and document to their requirements.
If I pursue public school, I'd probably wait until 2018-2019 school year "6th grade" to put him in Phys Ed with age mates. Although if they won't put him in 7th grade and let him take 6th grade Phys Ed, then I'd have to wait until 7th grade since in my state, 6th graders cannot accrue high school credit and he'd have to retake high school classes again for credit. However, I would have to put him into community college for math before then. If he progresses linearly in math, he'd be in Calculus by then. Once he gets to community college he definitely won't tolerate going to public high school...
