It is worth appealing to the HMO for a single-case exception that would allow you to continue with your current therapist. The premiums are generally higher for these plans, but it may be worth it. Privacy is another issue. In many HMO plans, a diagnosis alone will suffice for the first 8 sessions per year. While it is reasonable to be concerned about privacy, especially for those in high-profile positions, this concern has to be weighed against the cost of treatment.
Harmful outcomes seem to be rare.
If money is not an issue, the self-pay route is certainly safer. Services that we provide at LCL, by the way, are free of cost and do not make use of health insurance. As part of our assessment, we discuss insurance related concerns with our clients when referring them to other professionals.