Yep, squeaky wheel is name of the game with insurance. I have experienced on the patient and provider side. Be a thorn in their side to get things done.
More and more I am seeing patients go outside the US and receive much faster & efficient care. I had a patient who went to Mexico for a breast biopsy because the wait was 5 weeks here. She had new mammogram, ultrasound, biopsy, cyst removal surgery and pathology report within 3 days and for less than her deductible in the US. She said the facilities were modern, with excellent care.
Many of my family members go to Korea for medical treatments now. Something like a lithotripsy for kidney stones is 1/10th the cost of the US and you can get in immediately for treatment. Self pay of course.