So just an update. I did not get an email back from Alan Korwin, but I didn't really expect to. I'm guessing he's a very busy man, and it's difficult to respond to every email sent his way. I have about a 25% track record of getting responses from people like him, but it was worth a try.
However, this weekend, I did speak with my defensive handgun instructor while at the range (he happened to be there) and I just got off the phone with my lawyer a few minutes ago.
According to my instructor, he said that the no guns signs having force of law is in the trespassing statute, not the gun statutes. Basically, by ignoring a sign, which is considered a reasonable notice, you are trespassing, and the property owner/operator is under no obligation to ask you to leave/disarm before calling the police. The police, in turn, are under no obligation to ask you to leave. They may ask the property owner if they wish to have you charged/arrested. His side note was that most places will simply ask you to leave. However, they do not have to.
My lawyer basically said the same thing. Though she clarified by stating that there could be a sign that says "No Green Bow Ties" and if you enter wearing a green bow tie, they can technically call the police and have you arrested, without asking you to leave. She also said that most businesses will ask you to leave first, but she knows of at least a half dozen locally that call the police without contacting you first.
Her recommendation is to look around the entrances of all private buildings you wish to enter. If they do not have a sign, you are probably ok, but if you are asked to leave, you MUST leave immediately. If you stop to argue, you are now trespassing and the police may get involved. In addition, she mentioned that some signs are very small, or in difficult to see places. She specifically mentioned some local malls that have their code of conduct posted in very small print at most entrances (some have no signs at all) and in it they mention no weapons. Usually there's a smallish 2in diameter sticker that has a gun with a red line through it. She said that her recommendation is not to carry in that place, though she said that you may still get charged, and the definition of reasonable notice may be argued in court...at your expense.
In other words, disobey no gun signs in AZ at your own risk.
EDIT: As has been mentioned, the specified "No Gun" sign is only applicable in bars and restaurants that serve alcohol. If that sign is not present, you cannot be charged under that particular law. However, if there is another no conforming sign, you may still be charged under the trespassing statute.