So today, I connected with the rein more. As she walked around/by me on the halter and line, I would pick up on the line until I felt we were mentally connected and she was ready to respond, and then I would release the line with strong intent. She stopped nearly every time! It was fantastic.
I started playing with releasing her into roundness as well, experimenting with what feel told her "stop" and what feel told her "self carriage." It was a great time.