Thanks for all the superb comments.

A couple thoughts.

AF is not a possibility. Alaska ended their partnership with AF years ago when Delta became a serious competition threat to Alaska in their base city of Seattle.

I am aware that BA does not have F from LHR to CAI. ( I should have made that clearer) We have learned ( the hard way) when we fly BA F to LHR and then connect to a CE flight to Athens that the shock to our jet-lagged system of downgraded comfort and space was too much.... we have now started stopping in LHR for the night and resuming the journey the next day...somewhat rested and ready for the " downgrade". ( In this case it may not work to CAI as BA shows only one flight a day leaving at night....and we need to make the connection with in 24 hours..... a sleep aid may be our friend here)

We are leaning towards BA at this time.