Would running the engine until the thermostat opens (identified by electric fans kicking in) help the situation? While the 'stat is closed, there is potential for airlock behind it, keep the radiator cap off and you'll see the coolant 'burping' itself while it heats up and expands. Then when the thermostat opens, you now have a single full cooling circuit rather than two circuits separated by a thermostatic valve.
Put some rags around the radiator cap to catch any excess coolant.