> The other unresolved problem for me is that it still requires the assumption that light is parallel i.e. the sun is (relatively) incomprehensibly far away, and that was not established fact at the time afaik.
It seems like it very recently had been:
https://en.wikipedia.org/wiki/On_the_Sizes_and_Distances_(Ar...
There are some Stack Exchange questions that give more background:
https://astronomy.stackexchange.com/questions/38892/how-did-...
https://hsm.stackexchange.com/questions/14722/how-did-eratos...
Pretty clever to use the illumination of the moon to figure it out!