The reason you have been getting no improvement isn't because the bit is too mild. A well-trained horse slows, stops, turns and gait changes with NO bit at all.
So consider this if you want helpful suggestions.... Do you do each of the following things and require obedience every time and follow up within one second with a correction if you don't get it?
On the ground after pick up from pen or stall before tacking up:
- Require horse to leave stall or pen at your speed and not barge past you. Correction for rushing: yank lead rope hard back and back him up then make him stand. Repeat until horse complies.
- Stop every few steps. Correction for less than immediate stop: yank lead rope hard back and then turn and back him up.
- Require horse to walk beside you at your speed. Correction for rushing: yank lead rope hard back. Repeat as needed.
In the alley while tacking up:
- Horse stands ground tied with halter and lead rope and does not step forward or back or wave neck or bow down. Correction for each infraction with lead rope to move him immediately to correct position or walk him in hard circles or back him up or shake lead rope.
- Horse does not move when being saddled or is corrected sharply with lead rope.
Lunging:
- Horse complies with all gait change cues immediately without head tossing or rope pulling. Correction: for speeding up, whip noise or whirl of lunge rope; for down transition, lunge rope yank; corrections repeated more and more firmly until correct action occurs - without reissuing cue.
Mounting:
- Horse does not move forward or sideways. Correction, sharp yank on reins
- Horse does not move backward. Correction, slap on rump.
Under saddle:
- At walk and trot, horse stops instantly when requested through voice cue or legs open. Correction: half or full halt with reins as needed
- At walk, horse can walk one stride stop next and repeat at irregular intervals. Correction: half or full halt with reins as needed
- At trot, horse trots some small number of strides and drops to walk when requested. Also can trot some small number of strides and stops when requested. Correction: half or full halt with reins as needed.
If you answer any of the above "no", then you need to work on those, at least up through lunging, until the horse flawelessly complies.If you don't have compliance here, the bit doesn't matter because the horse's training and obedience is flawed at the foundation.
Now if these gaps are closed, once you are in the saddle, during training, when you need to use a half halt or full halt to correct a horse who is not listening for whoa or slow down cues from your legs, you may have to briefly use a harsher bit. But why not wait until you have the foundation in place and have no other choice?
The strength of the lightest horse has to be harnessed with training or the human will never win obedience. Your horse isn't "determined to have his way", he's been trained (maybe accidentally) to ignore cues and aids. You are going to need to focus on his training gaps (not riding) until he's obedient in all areas. And you will need to reinforce this training every day and every moment you're with him.
Excess speed is usually a sign of a horse who's afraid. What is your horse tense about? Are you pulling on his reins without giving him relief? Are you driving him forward while holding the reins? Do you continue to correct him after he complies? All of these can devalue the stop cue - any can make him afraid.
So think carefully and take a trainer's perspective. Your horse isn't a car with poor brakes. It's always a lot more complicated than that.