jb3t,
Setting the Spatial Reference of the map is not going to help you in your situation. The ESRI Basemaps that you are using are in WGS 1984 as you know, but they are also cached which means that if you set the maps spatial reference to State Plane then those base maps would not be usable because cached map services can not be re-projected on the fly by ArcGIS Server like non-cached services can.
So you have two options.
1. Make sure your map services that are State Plane are added to the map as ArcGISDynamicMapService's that way ArcGIS Server can re-project then on the fly to WGS 1984.
2. Add The ESRI Basemaps as ArcGISDynamicMapService's that way ArcGIS Server can re-project then on the fly to State Plane.