A further suggestion, which may be too much. UTM, and the various LCC used in the US at State Plane Coordinate Systems, have x/y coordinates that are nominally in meters (well, the older ones used ft or ftUS). Central meridian or standard parallel scale factors are chosen to make distance measurements on the ground correspond to cartesian distances calculated from project coordinates.
When printing UTM maps, standard practice as I understand it is to use a scale such as 1:25 000, where 1 mm on the map is 25 m in cartesian distance in projected coordinates. So the 1 km grid lines would be 40 mm apart. This is true even if the map is near the edge of the UTM zone (or in the center). So, it makes sense to treat a layout in UTM such that scale means the previous paragraph, even though it's off slightly from my previous suggestion. I view this as scale being sort of "snap to standard" if close. With quality projections, I suspect this is a difference that might not be perceptible, but in thinking of printed maps in UTM at standard scales being used with transparent overlay rules to read coordinates for search and rescue, I think it makes sense to be able to match this practice.
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