A, while your geometry is correct, I think you base assumptions could be wrong. The difference between a strike force hurrying and a full army +entourage travelling and scouting are very different things. Plus it was pretty common for the gem heart expeditions to get back after dark...
As for the military, remember that the listeners weren't trying to win, just survive. If they had riled the entire Alethi Nation they would have been completely wiped out in short order. I could give a pretty simple example for that, but it would be spoiler-full....