You are leaving her, which is good....but then you say that the LDS church is looking for a new counselor. You may not run into issues of your new therapist disclosing your information, but their advice is going to be very, very questionable.
I had been a Pastor for over ten years in a church VERY similar to the LDS. I can tell you based on experience and conversations I had with therapists in this sphere of influence, is that they will not make you come to peace with who you are. Rather, they will try to convince you that you are making a wrong decision. They will, in a way, pray the gay away.
They may tell you this up front or they may keep this from you but this is the driving force behind EVERY conservative religious therapist. I was there....I seen it happen countless of times.
Now that I am a liberal pastor, our church counselors are there to hope you find your way and to help you adapt to the issues you have. We also have transgender and gender therapists in our churches. They will never question the person's identity as what they see in the Bible. The only time they will question the path in which they are going is if that path is destructive to both them and their loved ones.
The LDS may send you to another therapist, but with the Mormon church, the therapy is going to have one course of action: to get you back on that right path and that right path is the recognition that you are not female (or whatever you are). If you aren't trans, the won't be able to even tell that to help you cope with alternative paths to give you peace. All they want is to bring you back to that glorious fold in heaven.
This isn't just my opinions or me just thinking out loud. I have been a pastor for over a decade. I pastored in churches from the Anglican church to the Assemblies of God church. I know how conservative religious therapy works because many used to work under me when I was a pastor in the more bigger churches.
See out a therapist who isn't tied to a conservative religion or a conservative political agenda. There are therapists out there who will only charge based on how much money you make.
Oh, and your new LDS therapist will say the same exact thing that your formal therapist did. They are not going to believe your trans status. They are going to think you are a boy who is confused and need God.
Matter of fact, I challenge you to do this: Your first meeting with your new LDS therapist, ask her or him "So, do you think I am transgender." I bet my year's salary that she or he will smile, nod, and say "well, we will work on that soon ok?" (or something eerily similar).
You really need to discern about this.