PS rereading, I see that I missed the point, sorry - so you've decided to go with the school, modulo some concessions, for next year, and are wondering about middle school. There I'd say it hugely depends how good the (2) middle school is in practice. Does it really succeed in stretching its most able students - will it succeed in stretching yours? I feel passionately that mathematically able children do need to be systematically challenged in maths all the way through if they are to achieve their mathematical potential - challenges in other subjects are really no substitute, and neither IMHO [humble in this one case because there are people I respect a lot who disagree] neither is recreational maths in which one has no pressure other than what's internally generated.
This forum seems to be very focused on acceleration - I think too focused. Given current educational realities, it may be true that it's generally the best that can be done, but that does not mean that it's the best that can be envisaged. There is enormous scope for e.g. doing harder problems based on near-age-level material, which I think is likely to be better for mathematical development than doing standardly easy problems on beyond-age material; but that's only possible with a level of guidance that doesn't generally seem to be available in most schools. If you have a school available that will provide that kind of guidance and challenge, I'd take that over acceleration any day, personally.
