Have you considered that in the single year your son may cover more than the K material and slotting him into school thereafter may be a problem from that angle too?
Of course, that is not to say that he won't do K and still have the same issue AT school...
I'm not sure what you should do, we are a homeschooling family and DS (7) admitted loving that "my teacher will always love me".
Most people here have had to consider Homeschooling even as a temporary option at one time or another, so you would not be alone and I am sure that as long as you could maintain a portfolio to show that he ticks all the school readiness (1st grade) boxes thereafter they won't say no to him.
