Flying in cold weather also helps with Fuel Efficiency. So, when Pan AM starts to make their return trip from London, they are now flying across and against jet streams and in warmer weather conditions which may explain the added fuel stops.
Airlines undertaking anything other than short journeys generally plan to fly at the tropopause, as that is the coldest part of the atmosphere. You are correct in saying that cold is good for efficiency. The problem with your argument is that, counter-intuitively, the temperature at the polar tropopause is actually warmer than the equatorial one, meaning that if you were choosing where to fly purely on the basis of atmospheric temperature, you'd prefer to fly in equatorial latitudes.
I also entirely agree with everything that stack, Duncan and Scomato have said. There are many, many things that simply make no sense at all about the model you have presented. For example, all of the issues that bedevil the north-centred monopole map are equally valid for yours. The enormous distortion of east-west distances causes all sorts of issues. Just look at typical journey times. It takes a couple of hours longer, for example, to fly from London to Buenos Aires than it does to fly from London to Los Angeles. But look at your map - according to what you've presented the distance between London and South America is far less than the distance to the west coast of the states. The USA on your map is also substantially bigger than Australia, which is completely at odds with what we know about those places.
There's nothing wrong with proposing something and then testing it against observations, but when those observations prove to be at odds with your model, a good scientist would go back and revise their assumptions - the world cannot be shaped in the way you propose.