As is often the case, the real answer is the monetize the solution. Charge for parking access / egress priority rights. Those in first class pay more, but get to exit first. The money problem solves how you get the resource for parking attendants, etc. needed to enforce the rules.
Now, you may even collect enough funds to make it worthwhile to improves the access to the local highways to increase flow rates significantly via additional lanes, etc.
A bunch of hippies won't like this solution, but they are probably used to it by now.