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...
There's a big difference between a private boarding school with lots of internationals and a public school. It's not an apples-to-apples comparison. Phys Ed wouldn't be my concern, more the social aspect of boarding where the kids spend significantly more time with peers in organized activities than at a typical day school. Supervision and behavior at boarding schools is also an issue, and while bullying may be less of an issue, early access to inappropriate material or alcohol may be more of an issue (in the UK this a problem; where we live it isn't). If the school gets kids as young as 11, they will be better prepared to deal with the age group than a school that generally accepts its youngest students at 13.
Others will have more experience with this, but community college does not in general offer rigorous math courses, nor are the (college-aged) students at a CC particularly mathy in general. Your boarding high school likely has more rigorous math than the CC, even if the CC courses seem to be higher maths. I would rather have a mathy kid in a rigorous high school course that may be slightly below level than a higher maths CC course that lacks depth.
