Our school district is the same way, must be 5 by Sept. 1 to start K, DS bday is in mid Oct. By chance I ran into a principal in our district at a kids party and he shared with me that there is a way to get around this. Basically you have to put in a special request, form hidden on schools website, after which time they test the kid. Assuming they past the test (never realized how serious these folks take the child's ability to cut correctly with scissors, lol) they are allowed early entrance.

The same holds true for someone wanting to skip K with the exception that you must be observed in the K setting for a few weeks before being moved. I say all this to say to be sure to comb thru your districts website and speak to as many folks as you can as there could possibly be an unadvertised way of getting this done. Good luck

-Guy