Robert, it sounds like you are already half way there. If you were to approach a family with the intention of showing the dignity and respect they deserve in their everyday lives, I would bet that they might say yes. Try to find an activity where you would not be in the way (harvest time is busy but full of life, a roadside stand, etc.) and ask if you can take a few pictures. Use a simple camera (35mm?) with a long enough lens to stay out of the way and you may be accepted. It might take more than one attempt, but it would certainly be worth the effort.
They get a bad rap because of their looks and strong core beliefs. For all of their austerity, they have a wonderful sense of humor and candor. It's too bad they are judged as a "group" without knowing anything about them as people and the values they cling so strongly to. Perhaps if more people lived as they do the world would be a safer, simpler, more civil place in which to live.