Just saw the current therapist. As it turns out, she IS covered by my new insurance, but after talking things over, she's given me an open-door blessing to try someone else. After how rude the therapist before her was, I was terrified she'd react negatively (basically get offended that I didn't feel our sessions had been helpful). I was so relieved when she was calm, polite, and just downright nice about it. I even told her about my preference for male therapists (something I'm moderately embarrassed about), and she was very understanding and told me that I had no reason to be embarrassed or feel guilty about it.
So, I'm going to try someone else (I'm currently waiting for a call back from candidate #1), but if I want to, I can always go back to her.
The idea of me being the one to terminate therapy makes me really anxious, but that went so much better than I had feared.
Thanks everyone for your advice.