Actually, I think I have the perfect way to handle it as an individual, if you want your voice to be heard directly:
Find an AMC theater with one of these signs posted. Go there, with your legally concealed weapon. Buy a ticket. Contrive to walk past the sign. Go back to the box office, and ask to see the manager. Tell the manager you want your money back, because having seen the sign you will no longer patronize this establishment, as your safety and the safety of your loved ones is too important to entrust to unarmed popcorn jockeys. Only ask for a refund once: believe it or not, you want the manager to refuse.
If the manager gives you a refund, you can still work with it, but it's better if you get to keep your ticket and complain that you weren't given a refund. Write a letter to corporate -- get it to someone as high up the chain as possible (but sending it to a department that handles business proposals will just make you look like someone that doesn't know how to follow directions and thinks he's "above the law"). Explain what happened. If you were refused a refund, explain that and send a photocopy of your ticket with your letter. Ask for your refund in your letter.
Thank them for years of enjoyable moviegoing experiences, and convey your regrets that you will no longer be able to patronize the establishment.
In my honest opinion, that's the way you're most likely to make an impact on someone in corporate offices that reads your letter. I'm going to keep an eye out for AMC theaters around where I live now: if I find some, I might just try to arrange an experience like I just described. I'm sure they'll be more attentive when you write in about a specific, concrete experience where you wanted your money back and decided that you'd never go again than if you simply claim that some hypothetical future trips to their theaters may not happen now. After all, a lot of people who write in letters saying "You're never getting my money again!" ultimately end up giving money to the people to whom they're complaining, anyway -- and the executives know it.
What's needed is to drive home the point that this isn't just theory. You're literally a paying customer, and not only will you no longer pay, but you also demanded a refund.
