In your situation I would have set the listing up in my own name as soon as I bought the property.
he probably doesn't want you to do this because you then have full control of the listing and if you're not happy with his services you can appoint another cohost.
I am a cohost and always have hosts set up the listing in their name so the host gains the reviews for their property.
1. Tell him to snooze his listing so he doesn't take further bookings
2. set up the listing in your name blocking out dates when he has booking.
3. you can then manage it yourself /use him as a cohost/ choose someone else to cohost