Actually I have seen a superior mirage do just that over lake superior.. Tom, you seem to fail at understanding refraction, temperature, or atmospheric conditions in regards to said experiments. Nor do you comprehend that only spherical Earth is going to give you the ability to show the Earth to be optically flat, concave, and spherical. This is especially true near ground level. And do note that light tends to follow the curvature of the Earth. The conditions posted in your "experiment" are actually prime conditions for said optical phenomenon. I suggest you study superior mirages more because those conditions you posted were very similar to the conditions from which I observed when I had seen a superior mirage over lake superior. You can in fact see over the curvature of the Earth (to a certain extent) giving the right conditions. So your argument here is useless. Especially when under average conditions no such phenomenon is observed.
btw, they can indeed appear to be no higher or lower.. However, even over a FE there is no such thing as exact in terms of elevation.. I suggest you figure out what hills, curbs, mountains, valleys, depths, rocks, cliffs, mounds, trees, grass, or even dunes are to understand your failure here. Do provide the data showing exact and perfectly flat Earth.