You're absolutely right that a rear will always be preceded by a stop. Horses just can't rear when their feet are moving forward, so the best thing is to get her moving forward, however you can. Since you can feel what she's thinking about doing, remind her to keep moving when she first feels like her mind is wandering. Spurs can help, but be sure that you have a stable lower leg and can control the spur at every gait. I would personally carry a crop, you can always drop it if you want to. Don't tap her after she stops, tap her when she starts to slow down into her "routine." Try to head it off.
Does she stop and rear on the ground? Does she really prefer one direction when lunging? Some groundwork may be in order if she does. Reestablish consistent and happy forward motion and willing directional changes on the ground, then at the walk, trot, etc. As always, rule out any physical reason for the behavior and be sure that she isn't reacting to pain or discomfort.
Do your best to not turn her around when she wants to just to pacify her. It may make her behave better temporarily, but all that she learned is when she gets bored, she can put up a fuss and then she gets to see things going the other way.
My guy will occaisionally do something similar at the canter, he just decides that he wants to be somewhere and throws his shoulder that way downshifting to a trot or walk, no matter what lead he's on. Sometimes we end up in a discussion, him half dragging us where he wants to go, me continuing to (vehemently) suggest that he continue the way we had been going. If I just change direction when he does, yep, he's got what he wants, and he learns that he can get it, no matter what I want. I work through it, get him back on track, and change direction when he's calm and listening. We both win that way, I just win first, lol.
Since your horse is more extreme in her behavior, I would suggest starting to turn her the way she wants to go, then follow through and circle her until you've done a 360 and are back on your way.
I hope that helps a bit! Good luck!
A stubborn horse walks behind you, an impatient one in front of you, but a noble companion walks beside you ~ Unknown