So I came up with this experiment today involving the change in distance to the sun, as well as the sunset in general. Basically, even if the sun appears larger from magnification, the outflow with respect to area to any point needs to remain proportional in order to conserve energy. This outflow, and therefore changes in distance, can be measured easily with a solar panel.
Therefore, I propose the following set of hypotheses:
Round Earth: The power generation for a near-ideal sun-tracking solar panel on a sunny day will rise sharply at sunrise; remain constant within a 20% margin throughout the day; and fall sharply at sunset.
Flat Earth: The power generation for a near-ideal sun-tracking solar panel on a sunny day will continuously increase between sunrise and solar noon; continuously decrease between solar noon and sunset; and have 2 points of inflection.
Null Hypothesis: The power generation for a near-ideal sun-tracking solar panel on a sunny day will not match either of the above models.
Before I go collect data for this, I'd like each side to confirm their hypotheses.