Lots of good points in Indigos post.
Do you have opinions from his preschool teachers? Educators like knowing that other educators concur with whatever they will be doing. So, if his preschool teachers strongly recommend he move into K and write a note to that effect it might help, too.
I'd start with the paragraph explaining that he has done three years of preschool and (if true) that he has always played and learned with the kids a year older? Stress his EF skills - compliance, frustration tolerance, works well in groups etc., - that would be a great thing for his current teachers to comment on in their note, as well. Don't make him sound too happy in preSchool - show that he needs more academic stimulation now. You write he has many friends, would most of those move onto K, now, too? (But don't make it sound you'd want to advance him only because of his friends). This is the place where a recommendation for his current teachers for acceleration might fit well. (You are not a pushy mom! You are listening to the experts!)
You sort of slide over his academic achievements, it is not very clear exactly what he is doing. You might want to go on then to describe a little but more about his current reading and writing, using grade levels for reference. I wouldn't be worried about mentioning first grade level - one year advanced beyond the grade you'd accelerate the kid into is commonly what educators like to see, and what, on the other hand, teachers, rightly or wrongly, think they can still differentiate in the classroom.
Stress a bit more that he is physically advanced as well, very tall for his age and hopefully as fast and coordinated as the other rising kindergarteners. Don't hide it in a list, make it an extra sentence or even paragraph. Again, something educators like to see. Stress his good graphomotor skills, mention what his teachers say about it in relation to the rising kindergarteners - don't just use extremely or excellent all the time, put it in perspective.
Then his ability testing, and what it means (ie he is not just a well trained hothoused kid of pushy parents, but his learning curve will remain steep).
Lastly, as indigo has already indicated, it's probably not a good idea to threaten "behaviours" if he isn't advanced. Stress that you are afraid he will be frustrated and unhappy, might lose his joy in school and learning.
Lastly, good luck! Our DS8 has done well with early entry, and he was by no means as socially advanced as your kid appears to be.
