I should have done my research earlier.
For simultaneous landings and takeoffs using VFR, the minimum separation between centerlines of parallel runways is 700 feet (213 m). For simultaneous IFR operations, dual simultaneous precision instrument approaches are normally approved on parallel runway centerline separation of 4,300 feet (1311 m).
Because the current separation between 28L and 28R is about 750 feet, I guess adding another 500 by swapping 28R with Taxiway C won't buy nearly enough separation to permit simultaneous IFR.