Every shooter needs to learn to do one thing and that is to pull the trigger without moving the gun. Single handed, double-handed, standing, from a rest, from a brace. Doesn't matter. You really shouldn't need to compensate for a push to the left with a thumb push to the right. What one must do is eliminate the push to the left. Make the gun and trigger fit your hand and then practice. This is not easy. One can learn to shoot a double action Sig or a revolver or almost anything with a heavy (but not gritty) trigger even single handed and not move the gun. But you can't do it out of the box on the first attempt. Not gonna happen.
Joe