It sounds like your poor son is desperately unhappy and under-challenged and I don't see how his behavior is going to change until his environment is changed. Imagine being forced to follow lock-step with other students 2-3 grades younger. It's got to be extremely challenging when his abilities are so much higher than his age peers.

Our school does two achievement tests for entry to GT, but we had private testing done as well after he got into the GT program because the HGT classrooms weren't enough on their own. Turns out it was the private IQ and Achievement testing that the school was most interested in because it was just so high.

Some ideas for right now:
1- Is this the end of a grading period? Since he got all A's, I wonder if you can be bold and ask the principal if he can try out 3rd grade for him right away, with an eye toward a grade skip next year. Ask the school to do a full evaluation for gifted and get the ball rolling on it right away. Ask for an Iowa Acceleration Scale evaluation in addition, so you'll know whether a grade skip is appropriate. Look around the Davidson database for supporting research about behavior and grade skips because I think you'll find some.

2- get some rigor into the classroom right away. Extra worksheets aren't enough. Can he start an online class right now? My son does AoPs at school and it's basically the only class in which he learns anything this year. For math, your son could do ALEX, IXL, CTY or many others. Maybe there's an online social studies or life sciences class he could do as well. This would be in place of what the rest of the kids are doing (that's how my son does his math-- the other kids get the regular curriculum; he goes online.)

2- get your son involved in something HARD outside the classroom, whether it's a musical instrument, tennis, gymnastics, golf, chess team, etc. Before we were able to make classroom changes for my son, he would often say, "thank goodness for gymnastics. It's the only place where I learn something new every time."

3- Find activities where he can interact with older kids who will get his jokes, and who will be interested in the same things. Is there a responsible middle school or HS kid who can work on a Lego Mindstorm with him? (You might have to pay them for this.) Or someone who can teach him some computer programming? My son is good buddies with older kids on his gymnastics team, and they've been valuable role models and friends outside of school.

It sounds like you have a really good understanding of your son. How about involving him in finding some solutions? When we had a frank talk with my son about his schooling, he was very receptive to hearing alternatives and helping making choices that he thought would work for him, and I'll bet your son would appreciate that as well.