In a very simplistic test I was able to do this by:
1. Creating an empty shapefile and creating a single rectangle that compassed all of the polygons to be labeled 2. Run the Erase Tool using the Input as the newly created rectangle and the erase feature to be the polygons to be labeled 3. Use the Maplex labeling engine and open the Label Weights dialog, increase the weight of the erased polygon to 1000, this should push all labels off the erased polygon layer and into the labeled polygons 4. Change the symbology of the erased polygon layer so it is no longer visible
In a very simplistic test I was able to do this by:
1. Creating an empty shapefile and creating a single rectangle that compassed all of the polygons to be labeled 2. Run the Erase Tool using the Input as the newly created rectangle and the erase feature to be the polygons to be labeled 3. Use the Maplex labeling engine and open the Label Weights dialog, increase the weight of the erased polygon to 1000, this should push all labels off the erased polygon layer and into the labeled polygons 4. Change the symbology of the erased polygon layer so it is no longer visible