I think the way the child feels about school is very significant. If you move him up a grade it sounds like that may not be enough.
Here's one suggestion for improvement. Find him something to do that he can be excited about at school. My DS did a few independent stuies all on his own last year. They gave him no guidelines and let him run with it. He told the gifted teacher what he did to learn read some books, made a diaroma, watched a movie on Brain Pop, made a quiz for the class and then he made a presentation to the class and gave out the quiz.
His teacher could also give him some breaks from the reviewing and then he could do alternate work that is related to what the class is doing.
Here is an example: at Math time if done early let him do sudoko Math puzzle or something else he likes.
I can feel your concern. Your son sounds much more advance than mine. I have read in some books that sometimes a little change can go along way to help a childs attitude about school when they don't feel challenge enough. Also explain to him why the teacher needs to repeat so much for the other children. I think patience come from more understanding others.
I hope you get some results with your school. When I first got our test results the tester just casual mentioned my DS abilitites and I totally freaked out that whole week. I wish you peace with this. Good luck
