What is the correct method for performing ablution (wudu') when madhy (pre-seminal fluid) continues to discharge before and after istinja' (washing the private parts)?

As long as the situation is as you described, that you do not know a precise time when this discharge stops, then your ruling is that of one afflicted with perpetual impurity (sahib al-salas). You should perform ablution (wudu') for each prayer after its time has begun and pray whatever prayers you wish with that ablution until that time expires. You should also take precautions by tying a cloth or similar over the area to prevent the impurity from spreading.