Literacy does not imply believing in the round earth. Proving the earth is round to yourself without trusting outside influences is not a trivial pursuit.
The theory only "holds together", with the assumption that everyone that works in any field even vaguely related to travel or communication is part of a conspiracy to hide the truth.
If you mean something else, then I have no idea. I'm not a proponent of the flat earth theory, nor am I a mind reader.
The experiment you proposed does not disprove the theory of a flat earth though, parsimoniously or otherwise.
It sounds like you may have rejected the notion of a flat earth purely on faith after all?
And yes, I reject all other evidence but this.
It also requires you being able to derive those equations which is more than many people would be comfortable with.
Especially if you think that "they" are lying to you, this could be a repeatable but cherry-picked piece of evidence that has a requires a more complicated explanation.
The math may be beyond some people but the effects at play cannot be explained by a flat Earth.
Part of the overall thread was along the lines of we should respect flat earthers, they improve rigour. It seems to me that the only sensible responses to that are the counter illustrations of just easily disproved a notion it is.
Far more effort goes into supporting this ridiculousness than did into establishing rough shape and size.