If anyone still cares (or ever cared), I found the problem. After acraptonofgoogling, I found out that the 360 doesn't feature analog
pressure sensitive buttons. The "shove" that I mentioned is the result of the 360 thinking my "normal" tap of the punch button was a "hard" tap. To fix this problem on the 360, there's an option to disable analog controls in the in-game menu. After doing this ...