Currently, it appears that a map service cannot be overwritten if any replicas have been created (i.e. any user has synced layers for offline use). It seems the only option is to delete and republish the map service. Which means you might have to re-create your maps from scratch. And for any users with replicas, they have to delete the entire map from their device and re-download it. This is way more complicated and time-consuming than it needs to be! Please allow map services to be overwritten and replace any existing replicas! Yes, that means that any updates will need to be synced and exported first. People are smart and will figure that out.
