Your horse needs retraining. Bigger bits is not the answer. Any horse can be ridden in a halter if your willing to put in the time and effort. People who don’t buy bigger bits and tie downs. It depends on how you want to train your horse.
My horse has a tense to run out a bit. I am now using a apple bit. It works so good on her!
I don't know if a bit but maybe try using another method to help it learn how to stop such as your seat and voice.
my horse is strong when on cross country so I use a dutch gag this helps as it puts pressure on the poll. try testing a range of bits:)
Multiple ways you could approach this fin he’s strong, there are rubber bits, rope noseband hackamores- which is a good alternative which can turn a horse completely responsive compared to with bits. Maybe try a trust bit too? :) good luck