So he doesn't have any backup code references? If he doesn't have a code reference to make you install AFCI, then he can't fail you. What he's afraid of is not knowing how to find the proper code. If he can't make the code say you have to install AFCI, then he can't fail you for not doing so.
Like it was said, distract him with coffee and donuts. Tell him if he can't find a code to prohibit you from just replacing the service, adding a few inches of wire to land them on the new breaker and bar terminations then he should feel comfortable passing your installation.
It doesn't have to be a judgment call.