We’ve had Cigna literally for a couple decades now. I really can’t complain. They have covered everything we’ve needed and my husband is expensive. They covered all our mental health also without problems. Much depends on what plan your company has.

Hugs, hope it works out financially. I'd check to see if you have any out-of-network mental health benefits. Ours (not Cigna) will cover 60% of T and p-doc visits for out of network (which both of mine are). If you get that, maybe she can adjust your rate a bit lower, so then it would work out about the same? If not, hope she's willing to work with you to charge you something you can afford. She probably would have been getting paid considerably less than her full, self-pay fee from the insurance company anyway (T and I were just talking about this the other day). So her reducing her fee for you wouldn't be as much of a loss to her as it might seem.
Lets hope not.

Hope that makes some sort of sense!