Let's get real simple here. If the General Assembly wanted a private owner's POLICY sign to carry the weight of law for TRESPASS, then the General Assembly would write a LAW that said so explicitly, as countless other states have already done. It's not a mystery here, I am quite sure that the General Assembly is aware that other states have done this, yet they have specifically chosen NOT to do it here in Virginia. That speaks with more authority than all the speculation any of us can muster.
And as previously suggested, replace the act of carrying a firearm with actions that others regularly do, such as bringing in food or drink, not wearing shoes or shirt, bringing in pets. As is too often the case, we are our own worst enemy on this topic. No sane person would advocate immediate criminal trespass arrest (without first simply asking to correct the policy violation) for someone bringing in a bag of popcorn to a movie theater. Or a teenage lawn worker, who dashes into a 7-11 for a quick can of soda without his shirt on. That is the exact same nature of policy violation as carrying a gun, and to even suggest that this should, on it's own, merit criminal trespass arrest, is ludicrous.
Imagine the consumer outrage over a theater having someone arrested for eating their own popcorn. That same outrage is what we as advocates for the normalization of defensive firearm carry should be prepared to bring to the table, but no, instead we worship the further discrimination of our own rights at the alter of private property ownership. It's not about private property ownership, or the right for the owner to make that decision. It's about making the owner UNDERSTAND that that decision is the WRONG decision.
TFred