Private property owners CAN post parking lots. Amusement parks do it all the time. Now, that being said, what about MPA? Well, the current thinking is that you're not carrying under your CHL while driving, the CHL exception isn't needed since carrying in you car is not otherwise illegal. So you CAN drive past a 30.06 sign protecting a parking lot, but you cannot then step out of the car with your gun. At that point MPA no longer applies, and the 30.06 sign comes into effect.
