Hi Magnum, it might be worth looking into this:
"doctor won't accept insurance" is not the same as "insurance won't accept doctor".
For a provider to "accept" insurance, they have to fill out a bunch of paperwork, jump through hoops, and spend a lot of extra time negotiating/coordinating with each insurance company they might bill. This has the advantage of making it easier for patients to figure out how their health care will be paid, but has the disadvantage of requiring resources that a small private provider might just not have available. Especially if they want to spend most of their time actually meeting with their patients.
Lots of times the insurance company will accept the doctor, however. (Not always, so check with your insurer.) This means that you go to the provider, get your services, and pay the provider directly. Then you take your receipts to your insurance company and get reimbursed for the amount that they are willing to cover. (Typically this is a totally legit use of an HSA, by the way.)
Sometimes the provider is willing to let you send their bill on to your insurance company and let you pay the difference, but, again, that requires extra resources that a lot of small providers just don't have.
It could be worth checking with your insurance company to see if they cover this particular provider, and how much.
I know the system of needing to pay a large chunk of money upfront, then wait to maybe get reimbursed for some of it is far from ideal, but if your insurance covers this provider and you can afford to have some money held in limbo for a while, this could mean you are able to see the provider of your choice.
I understand your frustration with the insurance options! Myself, I'm stuck on the super high deductible plan, where I have to nearly bankrupt myself paying towards the deductible before the insurance kicks in and pays anything. Each year. Basically it's only useful if I get hit by a truck. It sucks, but it's all I can afford right now. I hope this osteopath works out for you!