I think my problem was using the Custom Service style, rather than inheriting from ServiceControl. There are a number of ways to interact with the HostConfiguration.Service<T>() method and its overloads, but there's only one tiny section in the documentation.
TBH, I think you might want to deprecate that whole way of using TopShelf. Using ServiceControl is much much easier and better documented. I think if one wants to keep TopShelf out of their core code, it's easier to create a separate "ServiceWrapper" project that has a ServiceControl subclass and calls into your other code, rather than using the HostControl.Service() style.