When I got my first horse he had been left out in a pasture of a 7 year old girl. And he was as stubborn and denfensive as heck. He had a huge bit, and it took every ounce of my weight to get him stopped. I rode him like that for years. Of course I tried different things. He would ride with hackmore. (sometimes)
He was a good boy, but he was so braced all the time. I rode and loved him anyway. Just fighting through it.
Well after years and years, and hours and hours of training, and hundreds spent on professional training, he now rides in a super light bit.
I tell him whoa, and sit back, take pressure off with my legs and he will stop within 4 steps. No bit contact.
But being an older horse when I got him, and stubborn and set in his ways. Everytime I ride him I still have to do vertical and laterial exercises to make him remain supple.
He didn't get ridden much this winter. So he needs a refresher. I rode him last week several days. And it only took a little bit of circles and work to get him pretty light again.
But I feel your pain. To this day if I am cantering or galloping I still have some trouble getting him to stop. It's going to take a lot more time and patient to get it down perfect. But he has come a very very long way.
The just of the training is. Teach latieral flexion.
Then ride out at a walk. Sit back, say whoa. Take legs off. If they don't stop within 4 steps, take one rein and pull to laterial, applying leg pressure and make them do a few tight quick circles then ride out again. Keep repeating. It does take a while for them to understand. But my Toby hates extra work. And he knows if he doesn't stop when I ask him gently, he will be doing extra work by doing tight circles.
It took a lot more training and groundwork, but that is a main point. It's hard to understand. Heck. Maybe I'll have to upload a video sometime of how I work him. It might be helpful to others.