I thought this was such a beautiful story, I'm surprised that no one has commented on it yet! I can relate to how I think Elai is feeling during the journey to the end of the world - that it can seem extra lonely occupying the same place as other people, in this case the caravan, but in a completely different space. It can be worse the more people who are around you. The loners pestering her reinforce the isolation because it is clear that they aren't interested in her as a person. I think it was relatively easy for Elai to become acquainted with the narrator because she thought at the time that their relationship was for only a finite period.
At first I wondered whether the giants were a metaphor for the near loss of something real in our old west, like bison, but in the end, I think it was something entirely different. I think it was why Elai was drawn to them. Encountering something completely other than you can expand your perception of the world.
I don't think Elai was ever really planning to jump off of the cliff. Walking to the edge, where doing so is at least possible, can make it easier to think sometimes.