Welcome aboard. Great little car, the GTS4. Pity the RB20 is so under-powered for it.
To your problem:
faulty fuel pump would more likely cause it to run lean, not rich.
O2 sensor is a possibility, but remember it has no effect unless you are at constant throttle and low-medium load, eg highway cruise. Test it with a multimeter - the middle pin @ the connector in the engine bay should show volts oscillating between 0 - 1V when the engine is run @ constant 2000rpm.
Engine management is unlikely, unless you have aftermarket ECU. Although they are programmed from the factory to run a bit rich.
Injectors - a possibility. If 1 or 2 have a bit of dirt caught in the needle, causing a fuel leak into the cylinders. Get them sonic cleaned.