The solution would be to turn off that basemap layer using minscale attribute and switch to your own mapservice that supports data at that level of detail.
I am not sure what more I can tell you, that I have not already said... Every layer has a minScale and a maxScale attribute in the main config.xml (that you can add). Or you can set the ArcGISTiledMapServiceLayer displayLevels attribute. To do any of this you will have to actually add your basemaps in the main config.xml and not just use the addarcgisbasemaps=true attribute, like this: