Are there any websites that provide information on health professionals who DO accept patients' health insurance?
The only relevant website for you is probably your insurance company's website, which probably has a searchable list of doctors who accept that insurance. Websites that just display doctors who do accept insurance in general... I've never seen one and it wouldn't be useful to you, because what you need to know is which doctors accept YOUR insurance.
Any chance you can emigrate to Canada? I'm serious, it's a viable option in many cases, and not all that difficult for the well educated and/or highly skilled.