Thanks, everyone for all the answers, ideas, suggestions.

It's good to hear Alcumus now starts at Prealgebra, instead of at Algebra. That is the right level for DS7 so we can start it now. (He's only "offically" up to grade 5 maths, but I think he has "unoffically" learnt most of Prealgebra just messing around by himself on the internet.)

As to the AoPS online courses, I think he would need an adult with him, watching and typing. Has anyone done it this way? Could it still move too fast? I'd be interested in seeing AoPS's approach to these competitions anyway, as I'm not familiar with the American competitions.

ColinsMum, could you recommend some sources of problems in addition to Alcumus. We've almost never had DS7 solving (non-routine) problems at all, yet, as we were just getting him through the basic K-5 maths so he'd have some basic knowledge, but now he desperately needs to be challenged.

Another question, what's your approach to assessing "mathematical maturity" and readiness for certain mathematical activities? For example, I haven't mentioned at all to DS7 about theorems and proofs, since he's not ready for that. He can understand and explain things, but I'm just happy for him to think about things without worrying about rigor at this time. Know what I mean? What other stages of "mathematical maturity" should I be thinking about?

Another question, anyone know of a good resource (especially online) for learning very basic logic (and, or, not, quantifiers) and the same for set theory. These topics are totally absent from the school curriculum, so this void needs to be filled.

HowlerKarma, I certainly share your concerns about Virtual Schools (and thanks for your various warnings). At least they allow significant multi-grade acceleration, although these are just courses for average students.

As far as planning, we try to make it robust against unforseen changes. The timeline is a reasonable estimate, but it could change a bit. Actually, once the high school courses are reached, and progress is (mostly) locked in at one course per year, then that'll be the time to branch out into many supplemental activites such as AoPS. This thread should be about not only what you do when you run out of school-provided maths, but also what extra things you do before you run out.

As for college "planning" obviously we don't know what options our son will have, and that uncertainty is not really an issue academically. But financially (in the US) it's a big deal. With our modestly above average income, the best universities are the cheapest, since they offer the most need base aid (with the possible exception of state universities within ones state, which may be cheap but not good). I did a comparison of costs at Princeton and MIT using their online financial aid calculators

https://npc.collegeboard.org/student/app/mithttps://swebapps.princeton.edu/FinAid/finaid_form.pland found that, with our numbers, MIT cost $11k/yr more, and most places would cost more still.