I have to admit that one of the reasons I had for trying this approach was because of the competition thing. It seems to me that it is fairly standard practice to accelerate gifted math kids one, two, or three levels while still calling them a whatever grader. Do the math competition people make them compete at the higher level?
In the UK the maths competitions are all done by which school year you're officially in, not by how old you are or what you're studying in maths, so in that sense you're right, keeping him officially with agemates would be a win. The IMO, the ne plus ultra of maths competitions, says competitors have to be both under 20 and not enrolled in a university or equivalent. I've often wondered whether that rules out dual enrollment; this would be a thing to check if your child might be going that way. (We don't have dual enrollment, but it's certainly the case for some young mathematicians that they have to choose between being competitive in the IMO and going to university full time early. I noticed, for example, that Arran Fernandez, who was in the news a few years back for being at 14 the youngest student admitted to Cambridge for a very long time, competed - for Bolivia not for the UK (dual nationality?) - the summer before he went up, and came around the 25th percentile, i.e. did not terribly, but less well than any of the UK competitors. Had he stayed in school another 4 years, I'd assume he'd have done much better, but he obviously judged it better to go on to university. This may well have been a good call in his case, but in general it's a tricky area, because it's very easy to qualify for university by being able to solve routine problems only, where competition participation develops ability to solve hard problems. I can think of at least one other person who went to university early on the strength of doing school exit exams early but did not have anything other than routine maths skills; that seems a real waste of opportunity [ETA since he was reading maths at university, I mean!].)
For the earlier competitions, there's a sense in which it doesn't actually matter as much as you might think, just because maths achievement is so decoupled from age. None of the (UK at least, and I think it's the same in the US?) competitions set a lower bound for age or grade, and in practice, a large number of competitors are many years/grades younger than the maximum age/grade of the competition (the last competition DS9 did, and did well in, was open to some 19yos, for example). Typically, these competitors don't (and shouldn't according to Richard Rusczyk for example) carry on doing competitions until they age out of them; having done very well once, they move on. So there's a crude sense in which, if you have to ask, you aren't competitive anyway; and in that case, why not just do each competition for fun whenever you qualify and not worry about it? (I suppose one might be concerned that it limits opportunities to use competition success to help with college entrance? But this is a completely general concern: accelerating carries the risk of not shining by comparison with new apparent peers. Usual options apply; live with it, or don't accelerate that much, or decelerate at the end so as to shine then. Specifically for maths competitions, if you end up doing well in a "terminal" competition, noone's likely to care how you did on earlier ones.)
