Looking at this a little more i think there may be a solution. The stackoverflow post above would only work if you could get hold of the OpenGL SurfaceView itself, which we dont expose.
However, we do provide a method to get the current mapviews image which you can combine with the top level views image returned from the normal view.getDrawingCache method which you have posted above (this is actually what you would have to do if you did get an image from the SurfaceView anyway).
Assuming you are using our 10.2.7 release (not the quartz beta) you can do this with the MapView.getDrawingMapCache() method, here is the doc:
https://developersdev.arcgis.com/android/api-reference/reference/com/esri/android/map/MapView.html#g..., float, int, int)
w.