I think you hold him through the deadline, in case you can use him to facilitate a deal as the 3rd team and pick up an asset.
After the deadline, if he wants to go away for any sort of savings, you might as well - especially if it's tank time. Builds goodwill to let him go sign on with a contender, and doesn't hurt us.
He's also had some health issues, so it could be a win-win to give him lots of time off and showcase his skills in limited action. He'll appreciate, it'll increase his value, and it supports tanking to not overplay him...