To help understand why the overheating happens when you switch off is, as soon as the engine stops you have a problem called 'heat soak'. Engines get HOTTER when they are switch off. If you have a weakness in the cooling system i.e. a loss of pressure then the water will boil. This creates steam which will force itself out of the cooling system where ever it can so the pressure falls and the water boils ad infinitum.
Often the threads in the radiator are poor/worn/weak and this allows the plug to blow out, also the expansion tank is also known to split along one of the seams allowing water/pressure to escape as well.
Assuming you are getting all the air out and have no leaks then the head gaskets are suspect, perhaps you may need to have the radiator cleaned/refurbished as because IMHO all the rad/gasket sealers tend to block any and every hole they touch which also includes the heater/rad matrix.
The expansion cap should only be OE, some non OE caps I have seen fail to maintain the correct pressure.
Hope this helps
regards
Dave