Hi Earthmeasured, perhaps we can start with something I hope we can agree.
When digging a water well, one would dig it vertically. This is especially so when it is a deep well. It would be a badly constructed well if every time someone lowered and raised a bucket into the well scraped the walls of the well with the bucket. That would cause a lot of dirt (from the well wall) to end up in the bucket each time it was raised.
Further, the bucket would act as a builder's plumb, to anyone wanting to detect if a well was not perfectly vertical. One could use the bucket and rope around the edges of the well to check with high precision. This gravitational measurement would have been as accurate in Eratosthenes' time, as it is today.
Can we start by agreeing on this?