Kids remember the 2nd or 3rd grader who repeats a grade. No one remembers or even cares about he kindergarten kid who repeats a year.

My son's birthday is the day before the school year age registration cut off. He was SUCH a momma's boy, we knew there was no way no how he was ready to go to school. So we ended up keeping him back a year. He didn't need the services you describe, so he didn't do K twice, but no one at all cared about him being a year behind where he should've been. For boys, in particular, I think it works well. They get to be the first to drive in their grade, etc., instead of last.