Here is D Whitis' explanation for the skew:
"Mapping reduces the curved surface of the earth to a flat surface
representation. The UTM grid system of coordinates is most commonly used for digital mapping purposes. The UTM system breaks the surface of the earth
into many grid zones. Each grid zone "touches" the earth in the middle of
the zone. Grid north and true north don't align at all locations within the grid zone. Topo maps cover 7.5' of arc both N-S and E-W, and the longitudinal lines converge towards the poles (the top of the maps are narrower than the bottoms). Grid coordinates do not converge - they are square. The topo maps that fall towards the east and west edges of the grid zone must therefore be rotated most to align correctly with each other.
The DRG (digital raster graphics) map images are rotated to orient them
correctly to grid north so that when they are imported into mapping software
at the correct grid coordinates and scaling factor, which is specified in
the original files' metadata, they lap together seamlessly. For what it's
worth, the west end of the Grand Canyon is at the far western edge of UTM
zone 12S, hence the more severe rotation. The earth's surface is projected vertically onto the surface. The map represents the earth spheroid very accurately at the center of the zone, but there is some distortion near the edges."
I have yet to resolve this if I want to end up with a set of printable maps.