Hi Scully, and welcome from me too! The author of the Fibro Manual, Ginevra Liptan, is a functional doctor. When she says find a good doctor she means a functional doctor, not a rheumatologist. There are a few rheums who can help with fibro. But insomnia is definitely not their field. I do agree with her and many other functional docs that sleep is a great place to "start". But to get sleep better we'll have to work on the other symptoms like local pains at the same time, so you work yourself upward swinging from side to side (there's a kids' game that reminds me of with wooden figures between two cords).
Instead I'd recommend becoming acquainted with the recommendations for sleep of people like neuroscientist Andrew Huberman and Hugh Selsick.
Rheumatologists have been stuck with fibro because there are quite a few diseases that they can exclude that belong in their speciality. Fibro doesn't belong in anyone's speciality, so is simply dependent on doctors showing interest. My first rheumatologist didn't want to diagnose me because I don't look like fibro (I think he meant male and slim). My second did diagnose me, but was otherwise absolutely no help and had no understanding. She did me the favour of sending me to a rheum/fibro clinic, where I got to know 4 further rheums who knew I already knew which way to go, and could give no further help than that.
So like sunkacola says it's up to us to tackle our symptoms by ourselves with web/forum recommendations like here. Best if we can't alone would be some sort of mentoring scheme, and there are quite a few out there, but I've tested 2 or 3 and their competence is fairly limited, not up to a form of fibro as severe as mine or "patient activity" as high as mine, at least.
I'd also recommend you to stop amitriptyline. It didn't help me either, zombified me day and night, so my sleep wasn't restorative and I never really woke up. The 8th side effect was the last straw after 4 months.
You could stick around here and learn a lot what you can do. If you don't think that'll help, and you do need something else similar to Lipton, I'd be interested to know why, and encourage you to read/watch/listen more from functional docs, look out for them, praps at least try a mentoring scheme. And good understanding gentle manual therapists may help you more than most doctors, but again they won't know their way around insomnia.
If you want to get any other reason for insomnia excluded, I'd recommend a sleep lab, lung or psychiatric or both, for me the latter brought me a fairly understanding psychiatrist who thought outside the box, mentored me a bit in a sense, but that was luck, and he's gone. Aside from that for insomnia it was important to me to identify and minimize 30 triggers of it, to find supps that work - it wasn't the normal ones for sleep, and the last bit was using the recommendations of modern sleep experts, like Huberman & Selsick, for using early sunlight and changing sleep behaviour.
If you want to become more specific, this is a good place to do so.
For starters I suggest that if you are taking something for a sleep but it's not getting your sleep restorative, it'd be better to start on the alternatives instead. First inklings of what the sleep experts say: If you can't sleep, don't take anything, get up out of the bedroom not just the bed, and do something nice and calming all night until you can, until you are naturally tired. If you then still can't sleep after 10 minutes, start over until you can. (There's several tricks there to use, like Non Sleep Deep Rest audios as alternative and incitement.) And in the mornings, get out into the earliest daylight you can or a daylight lamp (I always prefer even the rainiest sky, just staring at that is brilliant for the brain and building up body melatonin so we have more in the evening.) Minimized screen time from 3h before bedtime onwards, including night shift mode. I didn't believe all this, but thought no harm in trying. They say gently pull your sleep forward to 10pm in small increments, that's not my style tho, to do it properly I have to wrench it, even if it meant a few weeks with less than 7h of sleep. It also showed me that I need less sleep than I thought, I feel better under than over 8 hours.
Loads more to be said, this is very simplified. Is that any help?