A natural setting for the Long Reflection:

Space colonization. If the speed of light is at all binding, then spacefarers will spend thousands/millions/billions+ of years in transit in a (likely) resource constrained environment. Why not engage in the Long Reflection then? 

This is especially relevant as these people will be able to restructure society as they see fit. This could also be a reason to put slightly more weight on space colonization as a pathway to existential security—it fosters moral progress & safeguards humanity.

Some might be concerned that space travel/colonization itself is something that should be reflected upon before anyone embarks on the journey. But this is not such a big obstacle. If our spacefaring long reflectors determine along the way that space colonization is bad, they can simply turn back home or, worst case, self-destruct.