[SAump]

4. Pitchers who hit three (3) batters in one game must be removed from the mound and cannot return to pitch in that game.

Your league president must now decide if the rule is worth adopting or not.
I never understood why a hitter would take a HBP off the hand, wrist or elbow. I would simply tell them to raise their arm out of the way.
A batter should not be allowed to wear elbow protection. They shouldn't be taught to dig in so close, nor to accept the rewards.
Yet, it may be better not to even say anything to the players who can't get out of the way. I enjoy teasing them after the laugh.