@stumpjumper: Like several other answers you have had above, some, but not all, my symptoms match yours. I was diagnosed with fibromyalgia about 18 years ago by a rheumatologist, and she was helpful in initial treatment with medications that took away some of the pain involved. This was at a time when fibro was still considered to be a "dumping ground diagnosis" (i.e. "not a real thing, but doctors give that diagnosis when they can't find anything wrong with you" - or a variation on that theme that I heard from several people, including one of my bosses). Right now, I take Celebrex (which is an NSAID) that she prescribed (but then moved away from our area - which is in SD - and we have yet to have another doctor to replace her) which is continuing to be prescribed by my primary care MD. I made an appointment in Rochester with Mayo in June 2015, mostly due to problems with restless legs syndrome, but I also listed in my top concerns (on a form they send you) the fibromyalgia. My first set of appointments was to a Sleep Center doctor, a Fibromyalgia Doctor, a psychiatrist, to a gastroenterologist, and a pharmacist (since I have had many negative reactions to several pills, AND, I wanted to make sure the supplements I was taking were doing some good and/or not reacting negatively with the prescriptions I was taking). I had excellent care and feedback from each department. All of those appointments occurred within a three-day period of time, and at the end, I had a plan of action and appointments to come back to the doctors who saw problems that were ongoing and need to be addressed. So, I encourage you to pursue the Mayo route as others have said. Especially, if you, like me, have been going to this doctor and then doctor or specialist, and feel like none of your symptoms are being addressed as a whole person.
I also wanted to add what I learned about fibro: the doctor I saw indicated that the current theory is that fibromyalgia is the result of several 'insults to the system . . . . and by insults that can be a surgery, a traumatic event, an accident, or anything that impacts the body in an intense way or has a significant impact.' When he said that, I could trace by the beginning of my symptoms to a year when I had finished school & had no job, was a single mother, and needed to have two surgeries in three months: a hysterectomy and a cervical fusion. Also,after my surgeries, a long-term relationship ended due to impatience with my ongoing hospitalizations, so in addition to worry about finances, there was this additional emotional component involved. I add all this additional information since it sounds like you may have symptoms of fibromyalgia, and possibly Chronic Fatigue . . . . it turns out that I had some of those same markers to justify a second diagnosis of chronic fatigue along with fibro. I also attended classes while a Mayo which spanned a 2 1/2 day period of time that spoke to exercises, medication, etc. I found it very helpful and affirming. I notice that John has referred you to another group that may provide you with support and ideas. Another issue that you mentioned that I also struggle with is the sleeplessness which is primarily due to my restless leg diagnosis. I don't believe you also have that condition; however, my Sleep Center doctor has told me that going long periods without sleeping (and I have had months and years where I have only been able to sleep two hours per night because of the intensity of the leg issues) can create insomnia alongside the reason for not sleeping. There is a Cognitive Behavior Class (CBT) that is offered at Mayo for people with insomnia - it is possible you could get some ideas from that. I do know that not sleeping exacerbates all kinds of other issues.
Good luck - I hope you find ALL the answers you need - don't give up though since I believe the answer is out there. Hopefully at Mayo.

Look for your microbiota. There is for sure a dysbiosis caused maybe by a SIBO/Candida/parasites

Check a kinesiology profesional specialized in gut diseases and dysbiosis