I completely understand what you are going through! My son, who will be 7 this Wednesday, just misses the cut off as well. Just as you, when he was younger, I always felt he should not be held back because of a few days. I even looked all over for private schools that would take him regardless of the September 1 cut off, but only found a few. He is now if 1st grade and could have been in 2nd if I pushed the issue, but I had a lot of people giving me what I now know as good advise!
Boys mature a lot slower than girls. Boys also have more issues with acceptance at younger ages than do girls. Boys grow slower than girls. Boys are more active than girls and require more outside time to exhaust their energy in order to learn and focus. For ALL of these reasons and more, I decided to put him in a private school and not push the age issue. Because I did that, he is doing awesome in school! He is ahead of everyone (for the most part). He still gets a lot of outside time, which they slow down on in older grades, so he can focus and do his tasks and listen and not interupt (which is the most important thing in a class room).
Now, I chose to put him in a private school so that he would never be held back. So, as he excells, they keep pushing him. They don't just keep him doing the same tasks as everyone in the class - he will get extra activities. However, it isn't segregated. Meaning, it isn't a gifted program. Again, that was important to me - not to be segregated because he was excelling. Everyone is equal!
Lastly, I am also a September baby (9/11). I started school earlier than I was suppose to. And I too excelled in school.....that is until I was in 10th grade. That's when it all catches up to you! The age of maturity and changing of you thinking process. The pressure from school that only maturity can help you get through. I was a straight A student until 10th grade and then graduated with a C+ average in the end.
So, from experience as a mom and personal experience. Put him in the grade/class he should be in based in the 9/1 rule so he can excell. And, more importantly, find a school that will not hold him back from excelling!
Good Luck!