I don't know about your part of the country, but here in NJ if we really don't like the AHJ, we can go to the " Court of Appeal." Which really is a set of 5 people who sit on a panel and they either decide in your favor or the AHJ's favor. These 5 people are usually made up of a Plumbing inspector, Electrical inspector, Building inspector, and a fire code oficial, and the last person could be almost anyone. A GC, and architect, engineer, etc. You might lose some time and it might cost you but if you feel that you are right you can take your chance.