On 2:
As you know, this is essentially what we did with our #1: 10 yo double grade skipped seventh grader with a grade 9 (algebra I) math placement. And it ended up being nearly 1:1, in an extremely small class, taught by a sympathetic university math professor who rostered exactly one class at our tiny private school, because the school couldn't otherwise offer math beyond grade eight. (And actually, that's what I did myself as a 10 yo 7th grader: HS math. But the HS was on the same campus.) It's not impossible that there is at least one other student in your preferred destination school who would benefit from someone teaching HS math.
On 3:
If you think DS can handle the greater EF challenges involved in a not-fully-independent study course, the in-school tutoring has the advantage that the school retains ownership of the process, which sometimes makes them more invested in success. And it's fully individualized, which is nice.
AOPS has the advantage of a likely higher level of rigor than off-the-shelf curricula. Especially if the in-school teacher hasn't taught HS math in a while (if ever).
At-home independent study: same EF considerations (although you can scaffold that more easily at home), and individualization advantages.
Might prospective HS be open to synchronous remote instruction? Laptop open with webcams on DS and the teacher, and the videoconferencing app of mutual agreement. Teacher offers classroom instruction per usual, checking occasionally for questions or comments from DS in the chat. DS submits assignments through their existing learning management system (which, at this point, nearly every high school in North America has). If needed, his in-person teacher can proctor exams and quizzes. Normal-quality earbuds with microphone should be sufficient to keep DS-end classroom background noise out, and keep the HS class from disturbing the local school environment. The two schools aren't in competition with each other, since it sounds like they have non-overlapping grades (and one might even be a feeder to the other), so there might be more hope of cooperation.
