Oh yes the "if you're not 5 you aren't allowed to attend" rule. :P
Oh how I hated that one! I called the private schools for miles away. I pleaded with administrators to meet him and look at his results.I searched and searched. He had suffered through 2 yrs of alphabet and phonics while he had been reading the whole time already. He really couldn't take doing it again but yet he was "too young" for phonics and counting to 100 in K. So now he would be reading for 4yrs before he could enroll and be "taught" what he had learned as a 1yr old.
Mine had been successfully enrolled in preschool for 2yrs with the group entering K and had full IQ and achievement testing (hitting the ceiling at 2nd grade level), missed the birthday cutoff by a month and STILL was not allowed to even do a trial of K. I was exasperated!
We did end up having a wonderful THIRD year of preschool before K. But K was really hard because now he was even further ahead... reading 5th grade and above, math 3rd/4th, science skills of a middle schooler, and geography skills beyond those of adults.
My advice is if you must enroll him somewhere (I needed to as we'd have driven each other crazy home all day) then try to find the school with the shortest day and most flexibility in grouping. Try to make friends with someone who really sees your child for who he is and will advocate for what he needs ahead. This has worked well for us. We meet soon to discuss plans for next year now that school realizes what a different learner he is than what they have seen before.
Good luck to you in working through your "gap year" before Kindergarten.