Picked up a Bigger Basic map today and judging from the map I got, it appears that folding four layers is a lot rougher on the map than three layers.
Don't know how the specific dimensions of 27" by 39" was come up with, but I think 30" by 40" (or any other multiple of 8") would have worked out a lot better. You could then fold it length wise for three layers then fold it back and forth an arbitrary number of times.
If the 27" by 39" was a magic size for some reason, then rotating the 8" x 10" tiles ( going from 8"+8"+8"+3" by 10"+10"+10"+9" to 10"+10"+7" by 8"+8"+8"+8"+7" would then allow five layers of three layers each and fold much better.