I already told you that the ancients could predict celestial phenomenas just fine under their flat earth cosmologies. The Ancient Egyptians had a flat earth cosmology and they could predict eclipses and transits decades and even centuries in the future.
You are saying it just fine: "
under their flat earth cosmologies". That cosmology is not the same as the one that Rowbotham and his followers propose. The "ancients" could safely ignore the fact that midday does not come at the same time in every part of the world and did not have sextants to navigate long distances, so the apparent shape of the dome of stars was irrelevant to the shape of the Earth.
Now things are different: Nobody, not even Rowbotham, ignores the fact that midday comes at different times for different places on Earth, and that means he had to change from a spherical dome of stars to a flat dome. And with this change he corrected the timezones but demolished almost everything else from every other cosmology known to man.
Even the Mayas and Aztecs saw in the sky an apparent sphere with the stars on it, and made precise measurements to that effect. Only Rowbotham and his followers defined their "cosmology" and conveniently forgot to make measurements to corroborate it. They predicteda whole lot of things.
Now, Please, Tom Bishop, give us a model that includes a flat sheet of stars and approximates what humanity has verified for more than 2 millenia. Even a drawing from any ancient civilization that shows a flat roof of stars will do.