I am not sure I followed all the detail. However, I don’t quite understand how things are improved by giving away a shared common property resource (the 3 parking spaces) to just a few owners.
I can see where your manager is coming from in that you need to be able to show that you are being even-handed. Perhaps you do that by cracking down consistently and simultaneously on all instances of parking that is not in designated parking spaces.
If there is anyone parking on common property while not using their allocated garage space for parking, then crack down on that. At the Tribunal, your argument is that they are diminishing the use and enjoyment of the common property by using for routine parking because they are not using their own garage.
If some common property parking is not causing an obstruction to other but you want to go to the Tribunal over the instance that is causing an obstruction, then that is your point of difference. Make it not about parking on common property in general but about obstruction of others’ access to their allocated parking.