Data.oregon.gov was just updated to include both Mondara and the Esri Integration Module (THANKS!!).
Data uploaded via Mondara is accessible via other maps on the site by using the 'Add Dataset Layer' button under the 'Layer Options' menu on the top-right of the map; however, maps added via the Esri module (i.e., ArcGIS REST Services) are not included in the list of available layers.
Furthermore, the 'Layer Options' menu on the map is not present on the web maps created through the Esri module, which prevents other data from being overlaid on the map view.
My feature request is to 1) enable the 'Layer Options' menu on maps generated via the Esri Module, and 2) include maps added via the Esri Module in the overall list of map layers that are available via the 'Add Dataset Layer' menu.
Erik these are great points and ideas. As you mentioned these are not available features now.