A lot off thermostats have a small, less than a 1/16, v cut in the inner separation plate. Many of the late model thermostats don't. For cars that seem to have a burp issue, I take an 1/8 drill bit and drill a small hole in the separation plate. The flat area between the thermal plate and the outer sealing ring. With that you don't need to remove the housing on initial fill. Open the bleeder on the stock 3800 housing, fill at radiator cap. Wait a little for the air to purge out and fill again. Start the car. While running, wait for the air to purge from the bleeder, close the bleeder. The water pump will "pull down" the coolant level from the radiator and "push up" the level in the engine. Top off the radiator. Reinstall cap and top off overflow
Because of the small hole in the separation plate, you don't need to wait for the thermostat to open. However, the coolant bypass hose from the intake to the timing cover must be functional.
I would also run the car, cool off, and top off again due to air trapped in heater circuit.
[This message has been edited by cmechmann (edited 12-06-2013).]