I don't think there is anything wrong with telling his teacher, especially if you feel it may give him a 3 minute leaway. I have told my oldest son's teacher because I was worried when we were in and out of the hospital about my son's mental state so I had her and the school psychologist on alert. It was fine, but we moms worry.
I doubt that talking to his teacher is going to change your craziness in am though. Are there ways you can streamline everyone's routine a little? Can you have her vest/nebs in her room ready to go as she's waking up? Or can you pack breakfasts (like lunches) for the car ride to school?
I'm a lunatic when it comes to being on time. From the first day of classes my kids know we leave the house at 8:30 -- which is WAY too early to get to the school 2 minutes away for the 8:45 bell. But still I follow that rule and even if we are "running late" we have never actually been late in the school time.
Another thing that might work is to rig the clocks in your house. Set them all forward 10 minutes, so that if you are on time, you are actually 10 minutes early. Maybe this will keep everyone moving and yet give you the leaway you need.