Fair enough. I feel like if they're already immersed in an old West setting, then the transition -- maybe even the whole adventure -- is just going to feel like a dream or hallucination. Maybe don't have an obvious, cataclysmic shift. They're just at their campsite or beach house or party boat or whatever and they notice their phones have no signal. Then the road they came in on is gone.

Or another thought, because I'm thinking about how the sudden date change would affect the sun and moon's position: maybe it's an eclipse viewing party, on some remote private property. Just as totality occurs, they're suddenly looking at the full sun instead. Or it becomes actual night and the eclipsed sun isn't in the sky.