Agreed. This is why we see so many real life country maps with "Not to scale" written somewhere. However, maybe we could fudge it by taking an average between the E/W and N/S distances on the maps, and make a scale according to that. For example, if your region is something like 440 miles N/S and 300 miles E/W, then you could make a scale based on a square map of 370ish miles NSEW.
The only side effect I can foresee is that the northern maps will cover smaller areas.
Here is a diagram that explains the idea. Notice the white squares are maps, and the yellow stretchy stuff is how they connect to each other. Imagine that they are wrapped around a globe and it makes more sense.



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