Doesn't Erastosthenes's experiment merely allow you to calculate the size of the earth if you already accept that it is spherical? As I understand the experiment it does not (nor was it meant to) prove that the earth is a sphere.
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.