Wikipedia (cringe to use, but here's more spaghetti against the wall) says the follwoing about Sea-Tac of that time:
The runway was lengthened twice, first in 1959 to allow use by jets, and again in 1961 to handle increased traffic for the upcoming Century 21 World's Fair.
Had to put in the part about Sea Tac.
I suspect when we get the airline data, we won't see the trip as having been through Europe and the East Coast. If my memory is correct, Vancouver BC was the Commonwealth airline hub in Western North America--flights from all over the Empire arrived there.
And that fits with another reported girl friend interview that says Ann was out of the country when he was born--she remembers in Canada.
According to http://www.vancouverhistory.ca/chronology1961.htm:
The switch by the worlds airlines to jets would mean a major overhaul of Vancouver International Airport. A figure of $100 million was cited. The city voted to sell the city's share of the airport to the federal government for $2.5 million.The Canadian government expansion of the airport for the jet age began in 1962. It is 232 km from Vancouver to Mercer Island according to Google Maps.
It's a lot of hops. Main BOAC planes in 1960s were the Bristol Brittania and the Comet. BOAC had its first delivery of 15 Boeing 707s in 1960.
There are other timetables and a couple of updates on the BOAC schedules between Aug 1961 from this 1960 page posted above.