Comment by aidenn0
Each pixel would represent roughly 16cm^2 using a cylindrical equal-area projection. They would only be square at the equator though (representing less distance E-W and more distance N-S as you move away from the equator).
No projection of a sphere on a rectangle can preserve both direction and area.
I admit it, I was applying Cunningham’s Law. Disappointingly(?), you came to the same answer.