There is basically no way to make progress here, as far as I can see. If the insurance companies weren't running open-loop before, they certainly are now.
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That's because they negotiated and paid for such a plan.
My sister works for a similar large employer. They hired Cigna as the insurer/benefits administrator, and every interaction is a problem. Your two kids have an ear infection? Cool, we've determined that the second one is due to an auto accident. It's so bad that the company hired another company to argue with Cigna for you.
End of the day, the employer controls the purse, and the insurer is doing what the employer paid for. It's cheaper to hire another company to argue for the folks who have noticed problems than to pay for a level of service.