There were British Airtours doing 707-336B trips to LAX into the mid-1980s. Were you BA mainstream 707 guys also handling the Airtours flights from Gatwick, or did they have their own crews (I'm conscious this might be a Tin Hat Needed type question !). I got offered a seats on an ABC charter on one. I presume these had the ability to go nonstop.
Slightly off-topic as the two BOAC 707-336Bs for the "Russiaway" service to Tokyo didn't get delivered until 1971, after the first 747s. There have been a couple of threads on here in the past about the oddball navigation procedures needed on those early Siberian flights