Hard to generalize but will do it anyways. In my experience, I've found more shoulders in northern US than south - and more in western US than east. Hence, when I pick a route going through the western US, I'm more inclined to pick a major US highway that stays away from largest cities and end up with either some shoulders or at least lower traffic. In addition, in west there are fewer roads to pick from.

When I tried using similar techniques further east (e.g. TN, MS, OH) then I more often ran into different combination:
- largest roads were fairly direct, but often didn't have good shoulders - and more traffic
- smaller roads had less traffic, but less likely to be as direct and still didn't have as many shoulders
So thinking from perspective of your preferences listed above, I'd either see if someone from southeastern states is familiar with these specific roads - or at least do some random sampling with google street view.