Let's address the root of the problem: Carry-on luggage..
Tolls, Fees, or taxation are a way to modify human behavior; thus carry-on bag fees are the way to go to restore order and civility to air travel.
E.g., $20 to check bag. $40 to carry on. FC, Prem Econ, and Elites have the carry-on perk; all others pay the man.
Problem solved.