Another possibility is to go to SCL (Santiago, Chile), but that likely means that you have to pay a Chilean visa fee, although you would have to do so for Brazil also. If you want to go to Mendoza, Argentina, for example, it's actually better to start in Santiago.
I don't think it makes sense that flights to SCL should have availability, while flights to EZE do not, given that the typical routing for flying on Air Canada to EZE would be XXX-YYZ-SCL-EZE, and the SCL-EZE flight is not nearly so full as the YYZ-SCL flight. But it's not like I have tons of experience with this.