WHBM
You have clearly described and precisely explained National Airlines leasing the two DC8-54F's from Airlift for their Miami to LHR route.
National Airlines inaugurated Miami to LHR on Tuesday 16 June 1970.
Bermuda II was signed by the US and the UK on the 23 July 1977.
To say that National Airlines "just sneaked in" is rather inaccurate as there was just over 7 year's between National Airlines being given route authority for Miami to LHR and Bermuda II being signed.
As you have already commented upon, National Airlines initially used the DC8-54F on Miami to LHR in 1970.
From 1971 National Airlines briefly used their B747-100 on the route, the airline had three in their fleet at the time having been one of the original operators of the type.
From 1972 National Airlines had replaced the B747-100 on the route by the DC10-30 of which they had five in their fleet which the airline had ordered for their expanding European routes that included Amsterdam, Frankfurt, London LHR, Paris Orly, Zurich.
On January 07 1980 the acquisition of National Airlines was completed by Pan Am taking over the airline's fleet and network. Pan Am continued to utilize the former National Airlines maintenance base and headquarters building until Pan Am ceased operations in December 1991.
Between 1970 and 1978 there were only three US airline's operating scheduled transatlantic flights between the USA and Europe, these were National Airlines, Pan Am and TWA Trans World Airlines.
Between 16 June 1970 and 09 January 09 1980, LHR had three US airline's operating from the USA which were the three listed above. This went down to two airline's after Pan Am acquired National Airlines on 09 January 1980.
Along with the passenger operations by the US airline's into LHR, under the original Bermuda 1 agreement it also allowed one cargo airline each from the USA and the UK to use LHR.
These were the following.
BOAC Cargo and from 01 January 1974 British Airways Cargo
Seaboard World Airlines and from 01 October 1980 with Flying Tiger Line after they acquired the former.
Incidentally Seaboard World Airlines were the first airline to fly a B747 freighter service between the USA and the UK.