Earlier quoted context omitted.
The sneaky thing to do is have your attorney send a letter to the insurance carrier's liability insurance provider, detailing everything you uncover and that they will be on the hook for the malpractice claim. That will get you an highly aggressive advocate with teeth.
What is a liability insurance provider? Are you saying Cigna and other medical insurance companies have insurance themselves?
An insurance provider for a specific industry has teams of skilled attorneys that are expert in that specific domain. Cigna might self insure if they consider medical malpractice a core part of their business. In that case, your attorney sends the letter to their corporate counsel.
Often times, day to day business people just ignore liability risks because it's not in their core mandate. But the corporate counsel is in charge of managing legal risk, and they will see such a situation as unacceptable. Corporate counsels also hold a lot of sway within a businesses structure.