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???
Pier 3 currently has 8 (Code E) stands, but several are split and can accommodate a Left/Right config for 2x Code C's or below such as 33L/33R, 32L/32R etc.
The buildings around the current pier 3 are crucial currently, they house the Airport's ID Centre and other administration offices. Not to mention a recently renovated brand new crew reporting building and associated staff security point too. Doubt these will be moved.
The ideal plan for reconfiguring Pier 3 is to actually get rid of just the connecting part of the Pier, and make taxiway Lima stretch all the way round to join Kilo by stand 31/15.
This would eliminate the cul-de-sac of both Pier 2 and Pier 3. So in other words, Pier 3 would be still the circle that it is, but with a taxiway continuing past stand 38 and probably going through current stand 31 on the other side to connect to taxiway Kilo.