Excuse my rather lame sketch but a rebuild of pier 3 seems feasible.
I don't know what the buildings around South Terminal are used for, and I'm not an expert on airport planning, but I can't see any reason why its not possible. Impact on pier 4 should be minimal.
Only problem I can envisage is accommodating the airlines that use pier 3 during construction. I don't know about gate availability at Gatwick - could they be shifted elsewhere or would it be a remote stand and bus scenario? With BA moving to the South Terminal a new lounge could even be built there???