Did you happen to read the description that I have given of Ambra thrashing and throwing herself around when the bit and bridle were on? This little horse is one smart cookie and over the years has tried every ruse to get out of listening and that was absolutely a classic effort. I think we give our horses far less credit often than we should. Just like you are trying to manage the situation, so are they because that is what horses do in the herd. And the whole thing, in my opinion anyway, that Parelli tries to teach people, is how to step into your horses life as the head horse. He tries to teach people how to not act like a predator. Just because you make your horse face their fears doesn't make you a predator, especially if you are being calm and supportive.
Besides, if JDI is having her horse square off to her when she is asking for more effort, maybe it is a case of a challenge and maybe if the horse is also pulling at the same time, maybe it did work a time or two to yank the lunge line out of JDI's hand so she could casually trot off and not do the task asked for. Or maybe you are right and in horsey language the horse is standing there weeping uncontrollably (in her horsey mind) and saying don't make me do it, I'm afraid of cantering. Although as to that one, I'll bet the minute she takes her off a lead line and turns her out she'll be cantering away without a care. But until JDI clarifies the animals temperment, it is kind of hard to say what she might try.