We got it today! She was stretching her head down low (without my asking her to) and she allowed me to maintain contact (instead of coming back up)
This was counter-clockwise. When we change direction, she wouldn't go past her normal headset (which is either straight necked or a little above her back) and she was much more forward.
This was all done at the trot. (our canter is the same in both directions)
Why is she like this? Is she lacking muscle on one side? Unbalanced maybe?