I agree with your idea and the principle behind it. Thing is a private entity is in their legal rights to infringe on your rights wether it be speech they don't agree with on their property or prohibiting your carrying of a firearm. So calling their policy "unconstitutional" may not be technically correct and may go so far as to give them the impression that you are one of the " I'm gonna open carry my Barrett 82 in Target 'cause its my right" peeps.
, and may put their minds on the defensive instead of opening them up. Just an observation.
But again, I agree with what you are aiming to do. I have thought of doing something similar.