Dave,
FWIW, I recently replaced the radiator in my sons' 1997 Lincoln Town Car (4.6 l V8) and it took quite a number of hours of running to burp out all of the air. 3 liters of air! And I disconnected the upper rad hose and filled the rad before sealing it up.
I recently learned of some air-powered vacuum cooling system service tool
that's supposed to make this issue a thing of the past.