We did sort of the opposite for our early October birthday kid, DD14. She started at a private school that had an end of calendar year cutoff date, and after 2nd grade, she moved to the public school. She was quite short and rather immature. The school gave her some quick tests and said she was academically ready for 3rd (and based purely on testing, that is where they would place her), but if we wanted her to repeat 2nd grade for social reasons, that was fine with them too.
We opted to repeat 2nd. Sure, she was likely bored out of her mind, especially since the private school was about a year ahead in math. However, this is the kid that I declared, "not college material" when she was 4. I later realized I was wrong on that one, but not until much later (entered gifted program in 7th grade based on FSIQ).
We later realized we were wrong on the sports side of things too. She is not super athletic, and while our kids have tried a lot of rec sports, husband declared that age 12 would be the last year in sports (even the lousy level of rec play) for her. However, two years ago in 7th, a friend asked her to try out for volleyball. She did and was a starter for the 7th grade (and next year, 8th) team. She made the cut for JV volleyball this year in 9th. She also asked to play travel softball. We had asked her many times before if she would like to try travel ball, but at a younger age when there were developmental teams (would have been helpful for her). However, she tried out for a local team and made it. She is now in the 3rd year of travel ball.
Sorry if this is long, but my point is that I wouldn't count out abilities - sports, academics, arts, etc. - based on early performance. I think that most bright kids are bored in elementary, so skipping pre-K or K probably won't serve their academic needs. While my three kids went to private school in early elementary, most folks I know say the public K is a waste of time from the academic side. Still, our district has very high test scores. SAT scores are on par with a lot of private schools in other areas, and with six colleges within 2 miles of our house, there are a lot of bright folks around here. There are many kids "waiting it out" until they get to middle or high school to see an academic challenge.
Of course, you may need to consider if the public schools will have other kids like him (possibly bored kids, but bright kids he can relate to). Here there are plenty of kids as bright or brighter than my kids. Staying back to be in the correct grade per birthday cutoff also likely allowed her to grow/develop skills in volleyball and softball so that she can play on the school teams. If we hadn't held her back, I doubt she would still be playing sports. Oh, and she still can't ride a bike, but that is my fault as I didn't teach her when she was young.
