So, are you arguing for or aginst FE?
I'm arguing that the variation of pressure with altitude (and by extension, the variation in the boiling point) can be equally well explained in both models, and that therefore the empirical fact that boiling point varies with elevation, alone, does not constitute evidence for either model.
This discussion is a good example of a natural phenomenon that does not give nice and easy demonstrations of the shape of the Earth.
While maybe we could construct measuring equipment that measures the pressure of the atmosphere with enough precision to differentiate between the two models (and I am using the term "model" very loosely in the case of "FET") there are other experiments and observations that give better results with a millionth of the effort.
If the FE "model" was right we should see a nice round wall around the known Earth, of about 70,000 feet high. That is several times higher than the Everest. And it would have to be surprisingly invisible. It would, as always, be easy to just travel South on a plane until a really impenetrable barrier is found. But it is easier still to make any number of experiments concerning navigation of a few hundred kilometers, on land, sea or air and tabulate the position of stars, sun, moon and planets.
PS. Remember, the atmosphere is a paper thin layer on top of a huge planet. It would not be wise to expect a stable enough atmosphere to measure such a tiny effect and not confuse it with other phenomenons, like the changing composition of the air at different altitudes.