I submitted a support ticket for the MapMyRide question over the weekend.
The response I received is that the Health app will only pull in calories from MapMyRide, and that Apple needs to make an update in order for apps like MapMyRide to "push" workout data into the Health apps (this is my interpretation of their response).
So sounds like perhaps in a forthcoming iOS update, that fitness apps will be able to publish workout data to the Health app. I've used the MapMyRide for ~ five years. Would like to keep using it and take advantage of the Watch's Health tracking capabilities, etc.