How 'bout Private testing? If he's legal in your state to enter K, then he's legal to skip to 1st grade, but without test results, I don't know if it would fly. If you can afford the Montessori or private GT school, I would at least investigate their programs to see if they're much different for K age (most school settings have playground, bathroom trips, songs, etc...I don't care much for it myself).
My youngest DS was tested shortly before he turned 5 and I brought the results into the principal. His skills were developed, which is always a concern with teachers/admin. He could read, write short sentences, basic math. Based on IQ and Achievement (skills), the principal let him go right into 1st grade (Note--none of my advocacy has ever gone that smoothely before or since). It has to be easy for them. Maybe pleasantly asking if they'd let him try two weeks in the 1st grade? Every school is different and maybe that's not at all possible at your school.