Regret is often experienced for difficult, important, and accountable choices. Consequently, we hypothesize that random regret minimization (RRM) may better describe evacuation behavior than traditional random utility maximization (RUM). However, in many travel related contexts, such as evacuation departure timing, specifying choice sets can be challenging due to unknown attribute levels and near-endless alternatives, for example. This has implications especially for estimating RRM models, which calculates attribute-level regret via pairwise comparison of attributes across all alternatives in the set. While stated preference (SP) surveys solve such choice set problems, revealed preference (RP) surveys collect actual behavior and incorporate situational and personal constraints, which impact rare choice contexts (e.g., evacuations). Consequently, we designed an RP survey for RRM (and RUM) in an evacuation context, which we distributed from March to July 2018 to individuals impacted by the 2017 December Southern California Wildfires (n=226). While we hypothesized that RRM would outperform RUM for evacuation choices, this hypothesis was not supported by our data. We explain how this is partly the result of insufficient attribute-level variation across alternatives, which leads to difficulties in distinguishing non-linear regret from linear utility. We found weak regret aversion for some attributes, and we identified weak class-specific regret for route and mode choice through a mixed-decision rule latent class choice model, suggesting that RRM for evacuations may yet prove fruitful. We derive methodological implications beyond the present context toward other RP studies involving challenging choice sets and/or limited attribute variability.