If he's already six, is he on the older end for grade? I ask b/c I wonder if that might help in advocating for placing him in 1st grade if he's close to 1st grade age anyway. Also, if he passed the district test for HG placement but didn't get into the program due to space constraints, I don't see as how they can now argue that he is not only not gifted at all, but near the bottom of the class.

I'd gather together whatever supporting documentation you have such as the district SAS test results, anything you have in writing from his K teacher from the beginning of the school year indicating that he was advanced (if you got any of that in writing), any other achievement test results, info from his preschool, etc. I'd then put together an outline of what you want to discuss with the AP and the points you want to hit on with goals for what you want changed (immediate placement in 1st grade with written agreement that you accept responsibility for the success or failure of this placement, or whatever else you think might work).

If you can, bring a supportive person with you to the meeting with the AP so s/he can help you stay calm and avoid crying, getting angry, or losing focus on your points & goals. Have a back up plan if they refuse your requests: moving up the ranks to talk to someone at the district, requesting a change of schools to a different school in the district, homeschooling with a letter to the superintendent & district GT coordinator as to the school's unwillingness to provide your child with a free and appropriate education...