Fine; rather than use x height and y width, let's just use road lengths. Those would be more practical, since we're talking about odometers. This way, we don't need to worry about straight trajectories.
We still need to worry about some trajectories. They would still be subject to distortion if you swap around RE projections. It'd just be more difficult for me to draw in MS Paint, but the point would be the same.
...distortion means that the road lengths cannot be the same in both the RE and FE maps
Or between two different projections of the RE map, for that matter. Road lengths apply to the Mercator projection, which is inconsistent with said roads' shape. If you use another projection, with less distorted shapes, you won't have accurate lengths. RE maps suffer from distortion issues as well. An exception to that is the globe, but that strikes us with another issue. Did people use globes to navigate the Earth while sailing? In most cases, they used maps, which were, to some extent distorted. Therefore, pre-GPS measurements were more than likely not to be accurate.
Do you think you could skip the "conclusion: FE is impossible" bit? You post it ever so often, and usually the argument you use to reach the conclusion doesn't entitle you to write that part.