The first thing i would do is establish if there is a leak, if your system is leaking you will always have issues with contamination (sludge), if you can convert it to a pressurized system then i would, but be aware sometimes putting a higher pressure in to the rads can cause water leaks on older systems, but as yours is only 6 years old it is less likely to be an issue, once you have converted then you can monitor the pressure, which will let you know if you have a leak and how big, if you find there is no leak then you can flush(if you flush and there is still a leak you will lose or dilute any inhibitor you put in the water to protect the rads), if you find you have a leak then as your plumber said you can run your pipework surface, or you can try to isolate different sections of your heating circuit until you identify which part of the heating circuit is leaking, also a plumber may be able to pressure test your system, cutting off each section until he identifies which part of the circuit is leaking.