Some good points raised by proudsceptic. Most likely your scheme has the minimum number of visitor car park spots as per the development consent, so that’s not an issue. Your main issue, as you mention, is that the visitor car park spots are filled with vehicles that are not owned by visitors. This is a very common problem is strata schemes.
If this is the case, there is no need to enter into a commercial agreement with your local council to monitor the car parking situation as your owners corporation through the executive committee should be enforcing the by-laws of the scheme.
Most schemes, including yours, will have a by-law covering parking. If your executive committee isn’t enforcing the by-laws of scheme, including your parking by-law, you can apply for mediation against the owners corporation. If need be, you can take the matter to the Tribunal for an order.