At my place of employment, the staff car park has a sign which states that all unauthorized cars parked there will be towed at owners expense. Each employee has a numbered sticker on their car that is registered to that employee. The car park has spot checks for unauthorized cars. Employees who abuse the parking loose access to the carpark.
So if it cave done for a company on their private property, why not strata? Have a big sign at eqch parking area clearly explaining that their car will be towed and tht they will pay for that. Each resident gets a sticker for their car. They have to register the plate numbers, make and model. Those with one garage/car spot gets to register one car, get one sticker, no matter how many cars they have. An owner with two garages can register two cars if they have them. If they only own one car they can only have one sticker, to stop anyone handing out stickers to someone else such as a friend who needs parking for the day.
But then there is the matter of the by law. As I have said before, as the majority of residents abuse or use the visitors car spots in my complex so there would be no way to get a by law passed.