Mad Friday tends to happen in places where the police are not!! Try the Houx roundabout or outside MB cmnp.
For the drivers parade, I would suggest get the tram into town, forget about driving. The tram goes from outside Houx Annex every 10 min or so and drops off near to the parade. get there early to avoid the hourdes. late tram run to bring the drunken rabble back until late, but again get back early to avoid these if you so wish.
Try a late lunch in town, find a good place near a bar and stay there for the parade.
Simon