This is an attractive experiment, because it provides a situation where RET and FET fly in the face of one another. Under FET, the higher you are, the closer you are to the Sun, the sooner it will set (as the angle needed to view the non-lit side will decrease with altitude: though the reduction may not be by much). Under RET, the higher you are, the further around the Earth you can see, the longer it will be until sunset.
There's an experiment outlined here:
http://arxiv.org/ftp/arxiv/papers/0812/0812.3911.pdfIt's to find the radius of the Earth, but you don't need to worry about that. Just note the principle: using an observer in a tall building, and an observer on the ground, you can time when the sun sets. Exact numbers don't matter: the question is which took longer?
There should be several seconds difference. It may need repeated experiments or more sensitive stopwatches/whatever timing equipment is preferred, but from that alone you have a zetetic experiment to perform yourself, to determine the shape of the Earth.
Plus, note that the linked to document recommends the experiment be used and taught in schools. I spy a hole in the conspiracy.
Any takers? Pretty cheap, simple, and could revolutionize all of science if you do it.