D-BOI:
My coolant system burping method is not very sophisticated. I put some gloves on and squeeze the upper radiator hose. It doesn't sound like it will work but it does. You will chase some air out. You can also try VERY CAREFULLY cracking open the overflow tank cap. This relieves pressure on the system and allows the coolant to surge into the tank as it expands. This is a dangerous thing to do since the coolant will be +200 F. Wear a coat and gloves.
Saner methods can be used.
1) Put the front wheels up on ramps so that any gas in the coolant system will rise to the radiator. This will work (others have done this and so have I).
2) On a cold engine, remove the two coolant sensors, clean the threads, put a little Teflon tap on the threads and install loosely. As the system heats up the sensors can be loosened a bit to let coolant seep out and the air to escape. Again, this can be dangerous so you have to be very careful. Once the air is out, let the engine cool and torque the sensors to spec.
3) Install a Prestone flushing tee. It goes in the hose from the heater (to the manifold) and gives a permanent high point vent.
I recommend the "front of the car up on ramps" burping method since there is less chance of getting scalded.
Before we get too far along, are you datalogging or just going by the dash coolant gauge? The dash coolant gauge is not super accurate (it is just a thermistor - resistance changes with temperature) so it would be better to datalog to confirm that the engine is running hotter and the fan is switching to high speed. Data is golden.
HTH,
Chris