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> I think I've only really seen this as a Honda Element - otherwise I'm not sure it meaningfully exists.

Maybe it's not meaningful, but vans in the 80s and 90s were often offered with optional 4x4, sometimes with a locking differential. An unmodified Astro or Aerostar doesn't have a whole lot of ground clearance, but could fit the definition of 4wd if properly optioned and probably wouldn't be suitable for these trails unless it gets some aftermarket help.

Of course, few of these are running anymore. 4x4 kei vans can get pretty serious too, but not a lot running on US national park fire roads.