The only reason I would trade Jeff Green is if it were a clear upgrade at his position (2,3,4). Garcia is not an upgrade and will not get any better (he's 29 and in his prime). Green is 5 years younger than him. Big Baby is somewhat equivalent to Thompson (Starter material), and I would like a S&T Davis for JT, but don't add Green into the equation. In his second year in the league, he averaged ~17 ppg, while Garcia, who I would not consider a sharpshooter or a great defensive player, at most averaged ~12 ppg. It would be as if we were trading Davis and Perkins/Nate Robinson for JT and Garcia, which is horrible.
I'm all for JT and Davis, which I think is a very good idea, but let's leave Mr.Green out of this.