My child was in the local public high school, but I found that I had to work out the DE classes on my own with the local colleges (both private and public). I called the registrars office, and got leads from there on how to proceed. Only after I had a contact and tentative verbal approval from the college did I involve the guidance office at the high school, since if I’d started with them, nothing would have ever happened.
Every school that I approached, both private and public, was willing to let the child take one class each semester there, either entirely for free, or just for the registration fee (meaning tuition was waived). If they’re willing to do it for any nearby high school, they’ll probably extend it to a home schooler. So don’t be afraid to ask! Your son could probably take the Physics at one school, and the Calc at another, and maybe even an English Comp or Lit class at a third, all at little to no cost to you, other than gas money and maybe a registration fee.