...following this as someone who works on both sides of the state line.
In Mississippi, the no-guns signs are usually the first question that pops up in a permit class. One sticky part has to do with trespassing. Once you walk past the sign, you are technically trespassing according to the AG. Whether or not there are any charges, depends on whether or not you get caught, how you react to it, how the business owner reacts, and how the police react if they show up.
No legislator so far has wanted to tell a business owner that their property rights are less important than the right to carry.
Another consideration is what happens if you end up shooting someone in self defense while in a place with the sign. The general consensus here is that once you walked past the sign, you were no longer in a place where you had a right to be and therefore fail one part of the justifiable homicide law. So far, I don't know of any cases where that was raised, but according to the state AG's office, it could come into play if the shooting was not a cut and dry situation.
That's my 2 cents. If yall decide to take it on, make sure the justifiable homicide language doesn't conflict with it.