I'm almost certain that if the Jays offered him a reasonable contract (Verlander type money, 180M for 7 years), he would have taken that deal, and remained a Jay. Yes, money does talk, but you can tell he enjoyed being a Jay; playing on an elite offensive team, playing in that atmosphere, and playing for an entire country. If you had a choice between the two deals, and also considering the chance of winning a World Series, which deal would you take? And honestly, does having a couple more millions really affect the outcome of your life? Being paid 27M a year would still set you for the rest of your life.
The fact that the Jays didn't even contact him, really pissed off a lot of the fan base, who finally got to see their team in the playoffs for the first time in 22 years.
As for him not being a big game pitcher, Kershaw had the similar label, until this post-season. Same goes for Randy Johnson, until he too broke label, when he won a ring with the Diamondbacks, at the age of 37, no less.