And I wonder if there are enough Less Wrong readers with friends with these diseases to make a survey of some sort?

That's not how you find patients a lot of patients. It makes more sense to seek online communitites where people with the illnesses congregate.

There's the patientslikeme forum: https://www.patientslikeme.com/forum/fibromyalgia/topics
http://www.fibromyalgiaforums.org/
http://www.healingwell.com/community/?f=24