Hamels and Greinke cost too much for rentals. Garza isn't worth what you have to give up IMO.
I'd give up quite a bit for Shields as a replacement for Jackson (offer Jackson the top-125 salary to get the draft pick and let him get his $50 elsewhere). Shields has team options of 2/$21 for the next two years, which is worth quite a bit, and I think playing outside of the AL East might mitigate his home run tendencies.
Dempster would be a good rental, but I feel like some team is going to be stupid enough to ignore that you no longer receive draft pick compensation for him and will pay more than we should. If they get the equivalent of Alex Meyer for him, would you really give that up for 2.5 months of Dempster? If the price was Destin Hood or Robbie Ray or something like that, I'd consider it. Same for Liriano, Marcum, and McCarthy.