We are in a similar situation, wondering about a mid year skip from third into fourth grade, at the end of which tracking decisions would be made.
The current consensus for us is subject acceleration in maths, no full skip. We may decide to do a skip at the end of the year into fifth grade of a gifted program in middle school. We have had some oddly conflicting test results which have confused the issue. Also, in our case, DS8 is anxious and has some executive function issues which make any change hard on him, so the idea is as few changes as possible - thus the transition skip, possibly. The school is leery of supporting a grade skip, and we are not confident ourselves what the right thing to do is, thus do not want to force the issue against the schools advice. It is a discombobulating feeling having to make this choice that so few parents have to make, particularly as most schools like to give you the feeling that it is a completely unheard of event and huge experiment and great risk blah blah blah.
In your case it sounds as if the school is fully in favour of the skip, which is rare and thus a great plus. It is highly unlikely they would advocate for a skip unless they were fully confident he'd cope. You'll probably be surprised just how much of the third grade curriculum he's got down already.
I would definitely set up a trial period, because it's good practice, not because a substantial number of grade skippers prefer going back to their old grade - most kids, once they have realized that the mind numbing boredom is substantially alleviated, refuse. But it removes pressure from everyone in the process, most of all from your son, who can be told that as he isn't learning much in second,he can try out third grade and if he likes it, you will ask the school if he can stay - no strings attached, just check it out.
The disconnect in math that you see may have to do with him understanding advanced concepts even though he may not be the fastest or most focused kids in doing addition or recalling maths facts, all that boring elementary school stuff that doesn't have to do so much with maths as a mathematician knows it.
