For the API call to MS Graph, BookingService. Add the availability values where there is a defining start and end (inclusive) time, along with custom hours or, bookable where free etc.
I have just ran into this problem as well. Is there any chance to get the custom availability on services to be a part of the Graph API call to the service? Currently, the only option I see would be to make a whole new booking business for each service that needs custom availability, which is far from an ideal solution.