Hunter rider here, and I hate teaching changes over a pole. It seems like a good way to make them late for dressage purposes as well because the jump tends to come from the front end first.
But I do think there is some value in teaching a really rolling forward hunter change sometimes in situations like this because you are not forward enough. It’s too advanced for this particular horse to figure out both collection and the mechanics of the change.
Work on the 2nd part (the mechanics of changing leads) for a bit until the leg movement is more confident, then you can add in collection. Yeah, a hunter rider gets off the horse’s back and may sometimes more or less throw the horse on the new lead with a shift in weight from a gallop and use the turn in this green stage, but some horses are not exactly naturals. But when I say “throw” I don’t mean “pull” the horse onto the lead because of course you don’t want to be doing it off the inside rein.
In the meantime, you can work on collection separately --do the simple changes (through WALK) mentioned above to teach that component of it separately. I like to use a serpentine for this and get straight in walk before the next upward. Try to shorten the amount of walk you need not only to pick up the new lead but to be really changing rein from the hind end first in walk.
