You may want to do some sound conditioning to help horse be more accepting of odd, peculiar or SUDDEN surprise noises.
We have found the Spookless CDs to be very helpful in this area. They are made for horse training in particular covering MANY kinds of sounds. I got a used CD player at Goodwill, put the CD on repeat play while horses are stalled. Sound was moderate to start, over several days. Then volume was louder as time went on. Horses came out to be harnessed, shod, groomed, driven away from the barn while hearing the noises.
No one had/has earplugs, never thought to use them! There also used to be noise tapes at music stores that contained many kinds of other noises too. Not sure if they still make those kinds of recorded things now. I carefully guard that tape!! Probably should try putting it on something more modern for easier use. Just a whole different class of loud noises.
A Google search turned up the Spookless site to purchase from. I believe you can read the noises on each of the CDs. If buying only one, I think the one we got was the Police Horse training tape for the most kinds of noises.
Something I learned about half-cheek bits, is that if you turn it so the cheek is pointing upward, add a bit-keeper to the bridle cheek, put the cheek in the other loop of bit-keeper, the bit always seems to work a little better.
Watching son ride with a ring snaffle with the half-cheek in the bit-keeper, there is less “time lapse” between reins and horse response, because mouthpiece is already in position on tongue to signal responsive horse.
Sorry if this sounds awkward, but any type ring-sided (D-eggbutt-loose ring) bit with a jointed mouthpiece, needs to have the slight slack taken up by reins before horse knows what you are asking. This is the “time lapse” mentioned earlier. Most horses have a little slack in reins to prevent continuous pressure deadening mouth feel. Taking up the slack has reins slide up the ring to get straight to the hands, mouthpiece slides to lay across tongue, THEN horse is ready to respond.
The bit keepers keep mouthpiece across tongue all the time, no need for bit to get aligned.
Changing to a bit (same mouthpiece) with cheeks creates leverage which the ring-sided bit does not have. So the way both bits works in horse mouth is completely different. Not using the curb chain on bit with cheeks kind of defeats the purpose of making bit stronger. Use of the curb chain will change how the joints fold in the mouth. Often are worse, joints poking up into top of the mouth, twisting because curb chain does not allow the same kind of pull as ring sides.
If your horse needs a stronger bit, use one! Being frightened you will lose control with your present bit is not worth it, takes all the fun out of driving. Then keep working for better obedience.
Personally I have nothing against direct pull, ring-sided bits. We consider them a step in training, with the final goal being a horse who goes well in a curb/leverage bit. We just think horse can do more things easier, in a curb bit. Some things are easier to teach them using the curb bit. The leverage is actually very minimal, rein in the slot just below the mouthpiece, curb chains in place, not usually tight. Our mouthpieces are solid, ported, thick, so horses are comfortable wearing it. No jointed mouthpieces here.
And we are back to horses ignoring science, mechanics, with some horses loving those jointed curb bits!! Ha ha