I think the Jays chances are actually being slept on here, and have been the whole time. The Jays are industry leaders on the splitter, and this is one of Sasaki's primary weapons. The splitter's rep for harming pitchers has made teams (for the most part) avoid it for a long time.
But the Jays can work with him better than any other team regarding how to better harness his splitter, make adjustments to the pitch, and throw it safely. Plus one of the things we know about what Sasaki is looking for in his team, is pitching development.
Having said all that, I still think he's going to sign with the Padres, but I also think reports are going to come out after that it was the Jays who were the runner-up, not the Dodgers.