My thought was to not have a basemap at all, just locally published map services. My application has no need for layers other than the services we are publishing, though I see that the projection is set by the basemap. So maybe I need to save one of our layers as a tiled layer and use it as a basemap for the sake of the projection? Would section lines be something one could use for that?
var service = new esri.layers.ArcGISDynamicMapServiceLayer('http://sampleserver1.arcgisonline.com/ArcGIS/rest/services/Specialty/ESRI_StateCityHighway_USA/MapServer'); map.addLayer(service);
           map = new Map("map", {                           });
Do you mean you don't want a basemap from ArcGIS Online, or you don't want a basemap at all? Do you want a completely blank map, or do you want some map data in the map? The base map does not have to be one of the Esri-provided ones, see for example http://doc.arcgis.com/en/arcgis-online/create-maps/choose-basemap.htm.
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