All they have to do is give him a place somewhere in the LEA's area. You will have to draw on your battle strategy experience to beat them at this game, start by asking the individual schools what place he would be on their waiting lists, they may tell you then you see where is worth persuing and where it is the equivelent of shovelling pooh uphill with a fork. If it helps, my mate who is a teacher, reckons one intensive hour with a quality tutor, may be as effective as a few shared lower quality class room hours. Just help him in the subjects you can in the mean time, and look for talented folks in your social circle who don't mind pitching in short term. My son helps loads of others with Maths for instance - he does get po'd when the teacher gives the kids she likes a better mark! That's life.
Keep on the right side of the Admissions Officer for tactical reasons, and it probably won't be too long as they have to provide that place - niceness pays if they encourage the school YOU want to squeeze him in. May the force be with you honey!