^An update to my earlier issue with the Python API — by changing from Hair to Emitter mode, and then changing the Frame Start and End properties both to 1, I’m able to export the static scene that I wanted.
Still not sure whether there was something I could have done in my Python script to access the actual state of the (not-animated) scene, while staying in Hair mode. It seems like a bug to me, but I’m still not sure.