Remember that you can always request an appeal or a "reconsideration" even with self-employed insurance. This is your best recourse.
Also, as difficult and as counter intuitive as it may sound, try your best to be "sticky sweet" to the staff. At larger public companies, these workers can get threatened with lawsuits, media coverage, etc, on a daily basis so much that they can become immune and disconnect to the members' problems and instead just react to their anger.
NCQA licenses these companies but this is not the route you want. They largely do retroactive reviews and are not as involved in day-to-day procedures.
Attempt to gain the workers' empathy and access all levels of available internal appeals.