The world went along fine when it was a Portolan map as well.
Sure but those navigators were aiming for large continents not tiny islands in a huge expanse like the Pacific Ocean.
But Captain Cook did navigate to the little island of Tahiti without problem and he knew nothing of you "non-Euclidean flat Earth".
He just accepted, probably without being aware of it, that he was navigating a non-Euclidean 2-D space embedded in a Euclidean 3-D space.
Or when we thought we could make salamanders out of fire. yeah, things get along fine even if we are dumb as a rock.
Irrelevant!
Man navigated across oceans and then built the statues on easter island.
But were they specifically navigating "across oceans" to find "Easter Island"?
Captain Cook was very deliberately navigating to Tahiti and Kingsford-Smith was very deliberately navigating to Suva and it vital that he find it promptly!
Your approximations are not as good as you think they are. They might serve you well for sailing and building big rocks, but that says nothing of their truth.
Really?
What evidence have you to claim that these "approximations are not as good as" claimed - can YOU do better?
Do you have a better map?
But Harry Lyons was not "sailing and building big rocks" but navigating a plane over the longest non-stop flight to date where the fuel usage was critical.
Over the ocean, there is only the occasional tiny island and he was aiming for the small islands of Fiji.
I would say that the simple fact that they did land at Suva was rather good evidence that their distance and directions were very close.
You really are a great one for saying words with nothing to back them up.