If Manny hadn't flamed out, and had finished here, you'd have to consider it. Orr and Brady are easy picks for me, championships, arguably the best player at their position in history, and the face of the franchise at the peak of the franchise.
Celts - I'll go with Red. He was the franchise until Pitino, and was still a part of the rebirth. (Influence on Pierce, brought Ainge back to hoops, etc.)
Red Sox - you have three options: someone before the curse, someone after the curse, or someone during the curse. Let's say you go with Cy Young pre (maybe there is a better pick, but I dunno), Teddy Ballgame during, the after is the hard call. Candidates should be franchise face and part of both championship. That pretty much leaves Manny or Ortiz. Given Manny's exit and his extended history in CLE (and whatever else.) And assuming Ortiz finishes here, plus the story of Theo finding him on the scrap heap, I'll go big Papi, but he's a bit too contemporary to have perspective.
I see the three players on the left, and Red looking in from the right, can someone photoshop that for me?