To me it's task #1 and shouldn't be too difficult.
Then, please, as a kind request, go out and map the world for us and tell us how it matches up with current models, without making any unproven assumptions about the world, since you have identified this as such a trivial matter.
You are saying you would accept my personal observations, thanks for the vote of confidence. Unfortunately, I'm not outfitted to do this, neither am I skilled in these mapping skills. People other than myself have already done this, will you accept their mappings and data in lieu of mine?
For now, I'll continue in this interesting project.
You are correct, unproven assumptions are to be avoided. That's why I have chosen things that are well documented. I have also carefully selected things that are easily verifiable for anyone that doesn't trust the source of the documentation. The documentation I have used is freely available on suncalc.org, timeanddate.com, and Stellarium. However, I'm always open to input. If you don't think the observations are accurate, please bring it up. I've asked before and you have not stated that you think these are inaccurate. I'll keep you marked as in agreement with the accuracy of the observations.
Update: I'm starting on a map using the below observations as guidance.
To review:
Current list of observations:
1. On the equinox the sun traces a very nearly straight line across the sky for every location on the equator.
2. On the northern solstice the sun is very nearly directly almost overhead at solar noon for every location on the tropic of cancer.
3. On the southern solstice the sun is very nearly directly overhead at solar noon for every location on the tropic of capricorn.
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.
5. For all points in northern latitudes, when looking due north observers see the northern pole star, Polaris. In the north polar region observers will see this by looking nearly directly up.
6. For all points in southern latitudes, when looking due south observers see the Southern Cross constellation. In the south polar region observers will see this by looking nearly directly up.
7. On the equinox the sun travels at a constant speed across the sky when observed from the equator.
Corollaries for Observation #1
a. Before sunset in Aranuka island in Kiribati the sun has risen in Ganggo Hilia, Indonesia.
b. Before sunset in Ganggo Hilia, Indonesia the sun has risen in Nanyuki, Kenya.
c. Before sunset in Nanyuki, Kenya the sun has risen in Macapá, Brazil.
d. Before sunset in Macapá, Brazil the sun has risen in Quitsato Monument, Ecuador.
e. Before sunset in Quitsato Monument, Ecuador, the sun has risen in Aranuka island in Kiribati.