Why not move Reyes over to 2B? It should hopefully improve his defensive value and assuming they actually get a good defensive short-stop, should improve the MI defense considerably. I think JJ Hardy would be perfect for this team, or if there is a trade to be made with the D-Backs for Didi, that would be good too.
Navarro can always been moved to back-up catcher, or traded. I just think his defense/pitch framing is terrible and his offense isn't nearly good enough to compensate for it. We don't even need to sign Martin to upgrade. Trade for someone like Rene Rivera (hitting OK and playing good defense for the Padres but stuck behind Grandal). It would be cheap, a defensive upgrade, and not much difference offensively to Navarro. These tiny upgrades will make a difference overall.
I'm drawing a blank on what the Jays could do for LF. There is not much out there. Maybe trade for Craig Gentry, stick him in LF, and hope his plus defense and speed will make up for his lack of power. He was a 3 WAR player with less than 300 PA's a year for the Rangers, so maybe he's a good buy low candidate if Beane wants to move an OF, but Beane is usually smart about players like that.
Regardless, if the team drastically changes its team building philosophy, they might be able to make up some ground in terms of internal improvement. Whether that's enough to make the playoffs is another story, but it's worth a shot. The all power/no defense strategy has failed miserably.