You're not gonna want to drive there....even if you rent a car. Parking and traffic will be a nightmare. Keep in mind....it's not like the parade takes place in a west-indian community. So all the west-Indians in TO have to commute there too. That's why I don't think it's necessary to be too close to the parade.
You would get on at Rosedale station....take it to Union station....then hop on a streetcar to go southwest to the parade. It would be a much longer drive than 17 minutes during Carabana. the subway will be full of revelers and will be fun in it of itself.