I would consult with an attorney for sure to make sure you are aware of any local and state laws and have yourself protected. Normally your PM should have a lawyer to refer you to.
Also I wouldn’t offer to give back all the money for rent as you have no fault and the issue was attended at a timely manner.
And also draft a letter you are releasing him from his lease commitment without penalty as he feels his health is at risk. You are taking his concern seriously and it is being investigated but meanwhile you don’t want anyone to live in fear for his health.
I don’t think you can evict him based on him being difficult but with a good lawyer and enough evidence on your end you can put your foot down and start dictating the rules.
I had issues with tenants and one of the issue turned out to be the PM, you need someone to be on your side and protect your best interest and not just a messanger. Make sure your PM meets that criteria.