I can't help you, but I'm interested in the answers you will get because we're in a somewhat similar situation.
My DS6 was skipped to 1st, but he already knows almost all of the curriculum so his teacher gives him independent work for him to work on when he is done with what the rest of the class is working on. Unfortunately, if it is at all challenging for him, he gets frustrated working on his own. I would like to have him subject accelerated so that he is actively taught closer to his level, because it is not working so well for him to be working independently when the rest of the class is being taught. Unfortunately, his teacher sees this as a sign that my DS is immature (well, rather, on par with the other first graders) and that acceleration to an older class is not appropriate (eventhough she knows he's academically ready).
You say that you would like to have your DS skipped to 4th for next year. Does his current teacher think this is appropriate? Would his teacher be willing to let your DS try out a subject acceleration for the last couple of months of this school year to see if him being actively taught new material might help?
I think it is, in general, asking a lot of a 6 or 7 year old to be an independent, self-driven learner of material that is assigned to them rather than self-selected. It's one thing to learn on your own at home when you can do it any way you like, it's another to have to learn on your own under the constraints of a school setting at that age.
