A couple of things to reference P2F's post as well:
I would move Grichuk to CF, sign a corner OF and trade Pillar.
I don't see Harvey signing here in Toronto and to pitch in the AL East. He'll likely sign a one-year contract somewhere like Pittsburgh or San Diego to rebuild his value.
Trevor Cahill would seem like a great fit here as a FA pickup. As well, if they could trade for Jon Gray, even better! I would even be open to Sonny Gray for one year if he comes cheap. Other options can be Ervin Santana on a one-year contract + incentives and Drew Pomeranz. I think Pomeranz signs as a SP. He was in Cleveland's system before, so Shapiro and Atkins are familiar with him.
As for the BP, I don't think Robertson would sign here. Plus he won't be cheap. Same with Herrera. I could see Cody Allen being a nice pickup on a one-year contract to rebuild his value, and again the Shapiro/Atkins connection might help to lure him to Toronto.
Trade Martin to the Dodgers. Could be a possibility with them looking for a catcher and I'm sure they would take on his contract if the Jays lets say took another contract from them (Matt Kemp maybe to play an OF corner and DH).