When mapping a single city, sun and moon won't matter at all. When mapping a continent, time zones predict the movement of the sun over time which speaks to distances between points on the continent. If you're mapping a planet, the movement of the sun and moon speaks to the size and shape of the planet. If your map is physically wrong, it will fail to accurately predict astronomical events.
I am able to use a map to drive from Northern Canada all the way to the southern part of South America with cloudy conditions through the entire trip so that i'm unable to ever see the sun, the moon, or even a single star. We are not talking about across the street. We are talking about millions and millions and millions of square miles which can be easily navigated by looking only at a paper map or series of paper maps none of which predicted the movement of the sun or moon.
Predicting astronomical events and cartography are two different things. Traveling damn near from one pole to the other does not require knowing what time and direction the sun should rise in the city 100 miles south of here.
Look at this system:
https://www.esrl.noaa.gov/gmd/grad/solcalc/sunrise.html
It predicts the movement of the sun. Can I use it to navigate the earth? Nope I sure can't. This has got to be the WORST map of the earth I've ever seen.
It seems pretty good at predicting the movement of the sun.
If you look at the observations that have been accepted so far it starts to constrain the map. For example, if you accept observations #1 and #4 as accurate:
1. On the equinox the sun traces a very nearly straight line across the sky for every location on the equator.
4. On the equinox the sun rises almost exactly due east and sets almost exactly due west for every location on the earth, except for the polar regions.
Then the equator must be straight line east-west. There is no way to have that observation be true and the equator not be straight line east-west. This eliminates the AE map and all it's variants, but allows the bi-polar map and the infinite repeating plane.
Now, if you reject the equator being straight you also must reject observations #1 and #4.
By keeping the observations simple, easy to understand, easy to verify, and non-contentious rational people can have a discussion about it.
So far, we have a beginning: all points on the equator are on a straight east-west line. There are no bounds on the distances, but the relative east-west positions cannot be rearranged. If people wanted to contribute instead of whining, I think we could make some interesting progress.