I use a single-jointed eggbutt and a grackle on Ali for dresage (grackles are dressage legal over here) and I do have fairly good control even though Ali is a very strong horse
Try a drop noseband. I swapped Baron from a flash to a drop for schooling as he tensed his jaw in a flash. Difference was amazing.
Also I used to hack him in a dutch gag, now I just leave his loose ring french link in, I have a lot more control with the drop so no need for a stronger bit.
Depends on the horse. I've known it work really well but when I tried it with Jim it made him even worse because he hates any pressure on his face or feeling restricted - for him a stronger bit used lightly is a better way to go. Even doing his cavesson up snugly will have him setting his jaw & fighting.
I agree with trying a drop, my pony also didnt work well in a flash but i find the drop brilliant for extra control, well when im the one sitting on him!