Well, finally something clicked. I figured out the connection to the outside rein. And Spirit's figured it out too. We are both on the same page, and with enough consistency to know it.
I certainly used to *think* that I had contact on the outside rein, but now I realize I did only for chunks of time. Then I'd just give it without realizing. I'd put her on the outside reign in order to get her to bend, or to do transitions, or when half-halting. But behold - keeping her on the rein all the time makes all of those things so much smoother and faster and better quality! Not to mention all the "in between" of just going around in a balanced fashion, with impulsion that is compressed. And now we can WALK! No longer is it the gait of loose reins and lackadaisicalness - it is a true gait.