How did the likes of Britannia Airways and Southwest Airlines deal with the FE question when they briefly operated Boeing 707s and 727s
Can't speak for those airlines specifically, but one way was to train the FO as an FE - in fact for one airline I know that used to operate 3 crew aeroplanes, you would spend the first 6 months as an FO sitting in the middle seat "working the panel" before being allowed to operate the aircraft proper. For more experienced crews, a coin flip or some other equally acceptable method pre flight would determine who performed which role.