I tried fixing her through “work at the gate, rest away” but it didn’t really work for her - she would march towards the gate and happily start cantering small circles. She has a lot of energy and endurance so it wasn’t feasible for her.
'Gate sour' is a horse's way of expressing that they don't want to do whatever is asked of them in that place - they aren't enjoying their 'work' and want it to end. So, among other reasons, I don't agree with making 'work' more unpleasant for them for this one either. That you've got 'varied & dynamic', sounds like she is enjoying that, so great - sounds like this has mostly worked for this horse. And if you want to change the *attitude* that is the cause of the 'gate sour', making 'work' in the arena fun & rewarding for her is important.
Does beautiful lateral work, turns on haunches and forehand, leg yields. But I didn’t ask her to do them. I asked for simple forward. If it makes a difference, I have no idea where she learned to do those figures.
Haha! She has known those 'figures' from birth. After all, virtually everything we ask of a horse is natural actions, but just put on cue, sometimes enhanced or exaggerated. So she is just doing them now as an attempted evasion. Ignore them & she will try something else.
So... how does it progress? Obviously, if she's doing well at faster paces, you do get her moving, but is that because you ask her to trot off or some such? Personally, I'd just ask her to walk on, and just keep asking, with that level of 'pressure', regardless what she does, until she eventually takes one step forward, at which time I'd *instantly* release and reward her for that. Rinse & repeat... pretty soon you'll get that step forward quickly, easily, reliably, and you can build on that.
ETA; after reading above, yes, agree with that tactic too, depending on horse's temperament - if that stresses them out more, turns those maneuvers into something unpleasant, then I'd caution doing it.