Created an account to say I really liked this story. The idea of dimensional travel is infinitely appealing.
Speaking of infinity, though, I do wonder if the setting of a Hamburger place as an inter-world nexus doesn't normalize some relationships that other-dimensional denizens might find unsettling. I realize that the choice of the "ordinary" and famliar location of a rural diner is probably meant to contrast with the fantastic/sci-fi premise, but still, the ease with which a supposedly diverse society of dimensional travelers intercts with our idea of a familiar establishment seems odd. For example, as a vegetarian I find it disturbing that, hailing from infinite worlds, not one of the guests would be disturbed at the prospect of killing a living animal, grinding up its flesh, frying it in oil, and eating it with corn syrup and food coloring. Or, along similar lines, all of the travelers seem familiar with and approving of the idea of employment, unequal ownership, monetary currency, and so on. Watt-Evans does a great job evoking a variety of vivid and intriguing home-worlds for the diners, but some things seem to deeply embedded in what we think of as normal to be able to imagine any kind of universe without them.
Fictionally, it probably wouldn't have worked to bring in these considerations, but philosophically, I find them worth thinking about. Maybe, as another commenter suggested, similar universes tend to glom together, so a shared world-view, even for humanoids from such different worlds, shouldn't be surprising.