We have yet to find a method of discipline that works for longer than a few days. Being sent to the office is no longer a deterrent, and being suspended for a day had no effect. ...
I believe E is incredibly bored and gets in trouble as an amusing alternative to sitting and listening or doing stuff he has no interest in.
One one hand, it's an unusual (male) 7 year old who can handle hours and hours of boredom, and the placement issues must be fixed. If homeschooling isn't an option (and it's a very expensive option to be out of the workforce for so many years, both in terms of income lost this year, and opportunity for growing future income) then it sounds like the options on the table are the school paying for a private school that focuses on project based learning so that each child can work at their own level and learn organically or a combination of gradeskips and subject accelerations.
Testing, done privately or through the school will help and give clues, but in my experience it isn't as though the testing is specific enough so that X finding can be treated by X schooling option. It's a long road of trial and error, with testing to at least rule out a few dead ends.
You son is very young, and you are right at the beginning of parenting him through school, it take a while to figure this sort of thing out. 2nd grade was 'the worst' for our family too. On wonderful thing about school is that a wonderful teacher might be just around the next corner. DS's 3rd grade teacher was amazing, and I would have been very happy to leave him parked with her for the next 3 years, but that wasn't an option. Look for teachers who are charismatic, self confident, and intelligent. Teachers with a sense of humor. Teachers who see shades of grey.
Then there is the discipline question. It is possible, at least with some kids, to get a discipline system in place so that they child doesn't complain anymore that the school is intolerably poor fit, but that wouldn't be my goal. OTOH, if you child is challenging in the home environment as well, then getting a system of discipline in place that you can live with that works tolerably well is to everyone's advantage. My favorite is found in a book by Lisa Bravo called 'Transforming the Difficult Child Workbook.' My son also found that creating trouble in elementary school was more 'rewarding' than doing nothing. It took a high toll on him, and now he sees that he can get more out of life by being decent to others, and that he has the self-mastery to do what it takes even when that is difficult. It is a little hard to tell if there is a discipline problem at home sometimes, because as a bright parent it's easy to see the potential difficult situations and steer around them - folks at school have neither the ability nor the desire to do that.
Thanks for posting, looking forward to reading your updates,
Grinity