I suspect you will need to offer him a graceful exit
If he is "working to rule" then he is probably no longer worth the higher salary you pay him, especially not the double which he earns relative to his formal manager.
You can't cut his pay without causing yet another negative reaction.
You can give him a new title, but that's not terribly meaningful if it is just created out of thin air. It also rewards cutting back on work.
If you are correct, some additional money wouldn't make a difference.
You can't give him the management position as he seemingly isn't qualified for it by rejecting all other management opportunities.
So the status quo is unacceptable, more money may not solve the problem, you can't give him his desired promotion as he isn't qualified, and a new title would be potentially meaningless.
However, you still need him and ideally would want to have him transition gracefully out of the role.
So your use your network to find him a new job with a non-competitior
Help him find a new job which starts in a few months (he shouldn't be hard to market) and until then, you can extract reasonably good assistance from the individual. Perhaps even find him a "Director" position elsewhere at a company which requires less management skill in their management. Make him a deal if you can.