In case you need a fact-check:
And, while it is true that the two pyramids have similar dimensions (at the bottom), the Pyramid of the Sun at Teotihuacan does not have a square base, it has a rectangular base.
The Great Pyramid in Giza is also twice as high as the Pyramid of the Sun.
Oh. OK, right, there's an Antarctica on the top asked the bottom, which means the no-land-mass North Pole overlays Antarctica.
OK, I see it now, thanks.
I still think this would be nicely done as a butterfly projection; I'm still uncertain about whether the distortion of the projection would affect overlap accuracy. OT1H, N/S are equally distorted, so maybe it all washes out? OTOH, I'm suspicious of Mercator projections. Do you know?
The Mercator projection only distorts N/S, and the distortion is symmetrical about the equator. So it shouldn't make a difference in this case. since corresponding points on both the right side up and upside down map are equidistant from the equator.