This is usually the result of a horse that has not been trained properly from the ground up. Fact is, my last rescue horse was like this.
The answer is NOT a stronger bit. The answer is not running the horse into the ground until stopping is a reward (that is just plain cruel). The answer lies in retraining the horse as if it were a raw 2 year old that had never seen a saddle or bridle or rider before.
Start on the ground. Use a proper lunge cavesson and side reins with saddle or surcingle. Teach the horse that forward requires thought and impulsion from behind.. and that walking has different speeds as does trotting. Transitions up and down are can be done in a impulsive, relaxed manner and that tracking up (rear end neither cramped inside or swung outside the track) is the easiest way to travel. Take your time. Lunge for 15 minutes (equal time both directions) starting with loose side reins (a little slack in the reins and a snaffle bit) at the walk.
Get a set of long lines. Long line this horse everywhere. Up hills, down hills, in circles, around corners, in figure 8's and serpentines. Walk walk walk on long lines. This helps the horse to learn to move correctly.
First ride.. after about 5-6 weeks of the above work.. in a small enclosure. Loose reins and use a leading rein.. do circles, change of direction, figure 8's, serpentines.. all this same stuff at the walk. Work into transitions.. extended walk to normal walk. Walk to stop. Stop to walk. All relaxed... and work into the other gaits the same way. No trotting for at least 2 weeks.. just walk walk walk. No trails. After the first week move to an arena. Work there. If the horse gets hot or fast, go back to the pen.
Horses that do not stop are usually not being true pigs.. they have never been taught anything about impulsion, working in a balanced manner and have been ridden front to back instead of back to front. They lack true impulsion.. the run through the bridle and are out of balance.
Horses that are true pigs about stopping are very very VERY rare. From your description, I doubt this horse is that sort. I suspect poor training.
More bit is not your answer. More training (of the right sort) is the answer.
There is something about the outside of a horse that is good for the inside of a man. ~Winston Churchill
) Dinosaur Horse Trainer