One thing that stood out to me in your description is that you said you made sure the click boxes "all display for the entire length of the slide".
Are you aware that the pause point for a click box is right at the end of its object as shown on the timeline? So the click box pause point is not shown the same way as for buttons or text entry boxes where you have a vertical line in the object to show the position of the pause point. If your click boxes go all all the way to the end of the slide timeline, then their pause points will be right at the end of the slide, not somewhere in the middle, which is usually where you WANT them to be. If all click boxes are added in the same way, and their pause points are all at the same frame of the slide, then clicking any one of them will unpause the slide and execute whatever action you assigned to that click box.
