So, just realized something. As a former teacher myself, I actually think part of the "immaturity" angle from teachers is that it's harder to differentiate for maturity than it is for intellect/ability. From a workload and managing the classroom standpoint, a child who is an outlier in terms of maturity often requires much more intervention in terms of one-on-ones and classroom management than a child who needs advanced work. I wonder if all of the teachers and administrators who recoil at the thought of acceleration are at least subconsciously afraid of this.
That doesn't mean that you shouldn't accelerate. But, it does mean that the teacher might need to be reassured that she's not going to be pulled too often from the rest of the class to deal with emotional issues. (For example, when you and your husband had to calm him down when his brother insulted him.)
Just a thought! Good luck with your decision.