@criver: In a normal situation it would be relative safe to travel at night in a known trail, given that there's enough light from the moon.
That there isn't any trees is the problem, they could hide in it's shadow during the day, and they could travel by night.
And you have to remember that the "road" is constantly changing due to the earthquakes and with the low tide, it's probably a 3rd or 1st quarter moon, not enogh moonlight to see really well. They probably don't want to risk walking into a sinkhole or something, last chapter the protagonist fell into a ravine, at night that would end pretty badly for them.
And yes, best case scenario is walking at dawn or dusk, they should rest during the day, but there's nowhere to hide from the sun. It's a "we get cooked in this place, or we risk it and walk while we get cooked" situation.