Ok, I am going to go ahead and aswer my own question here, in case someone else runs into the same scenario.
If you add a custom field to an application user profile, it will be automatically added to the id_token if the "profile" scope is requested. It is is that simple.
However, I have not found a way to define a custom scope that would return only a subser of the custom fields defined. But that is not a show stopper for me.