Take the BA flight . If nothing else you will have access to the CCR predeparture.

As an aside my most memorable flight related caviar recollection was from 2006 or so. Coming back from LHR around the time the liquid ban on board was introduced. Initially it was a US only thing and poorly governed. There was a second level of inspection as you boarded flights to the US. A woman had a tub of caviar that was disallowed for boarding. She force fed it to herself at the departure gate.