Has anyone successfully held their child back from Kindergarten?

Hi all, My son will turn five right before Sept 1st this year, meaning he should start Kindergarten this fall and be very young for his class. I know that Berkeley public schools won't allow me to hold him back and would send him straight into first grade if I waited a year. Nevertheless, for multiple reasons which I won't get into here, I want to give him one more year before starting school. Here is my question: has anyone held their child back from Kindergarten by sending them to two years (or more) of private school and then making the transition back into public school? If so, do most private schools accept young six year olds into K? I'm looking into it but would love to hear from anyone who has been through it already. Thanks very much!