I don't see any reason at this point to force a bad deal to satisfy the player's demand. At this point, if you keep the player and don't move him, I only see three possible outcomes.
1. He holds out, gets suspended without pay, and the league allows the team to remove his cap hit. That opens up the space to bring in another player.
2. He shows up to camp with a chip on his shoulder and plays well enough at the beginning of the season to generate interest in reasonable offers as teams around the league see him as being back to a level that interests them and creates a competition for his services.
3. He shows up to camp with a chip on his shoulder but struggles because he can no longer do the things he used to do after three surgeries on the same shoulder, and realizes that he either needs to shut up and give the team whatever he is capable of or decide he's had enough and LTIRetire, again opening up cap space for the team to bring in another player.
I see absolutely no reason for GMDA to trade him for whatever he can get before camp, especially if it means retaining a significant amount of salary and/or being burdened with a bad contract.