Larb- I tried out some graticule lines and do believe it looks better than the rhumb lines. And thanks for the suggestion to turn down the opacity of the lines, looks way better, I think

Gold- I have very little idea of what a map projection is. I guess I was trying to use whatever projection is used for rectangular maps of earth.

I do understand that the top and bottom of the map is stretched. Is there some other way I should draw it or something?

And thanks for pointing out about the top corners nearly touching on a globe. I might put a bit more ocean between them


Here's an updated image with graticule lines instead of rhumb! Opacity turned way down, is this the way graticule lines should look?

Click image for larger version. 

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I'm going to try some experimenting with the mountains and try to get them to look more like mountains