And how about using the vertical equivalent to a staircase runner on the doors as a temporary way to lighten them for the open house?

Stripping the trim will be hell. Stripping the doors would be much easier (particularly because they can be sent to a stripping place). Perhaps paint only the doors in a much lighter, wood-like, color, but not the trim?

I love older homes but really dislike dark wood trim. To me, it just makes the house feel depressing and dungeon-esque. While there clearly are others who feel differently, I suspect your realtor is correct--you will appeal to a greater number of buyers with white paint.