So I turned out all the mares, and then the first pair of geldings. By then, she had calmed down and even was picking at her hay. She haltered OK and we did some head-down and backing. I was able to lead her out on a loose lead - she stayed at or behind my shoulder, which is what I wanted. I did hear a few tail swishes but ignored that since she was behaving.
When we got to the gate, and I let her go, she did her "drop-the-butt-and-bolt-from-the-gate" maneuver, and chased all the other mares around the round bale just to show them who's boss!