I also use mine with a back quiver. Here is how I lessen the floppiness of the haversack. I put it on my shoulder and shift it around more toward my back. Then, I put on my quiver which helps to keep it from sliding back by my side. It is not foolproof, but it sure helps. One other consideration is that, if it is flopping a lot, you may be moving too fast. I have that issue, too. Also, over time, I developed the habit of walking with my left elbow tucked by my side, which further steadies the haversack.
While at the zoo, how about passing along to Theresa an idea I have had regarding this problem? Attach a short lead to the bag, that can be hooked to a belt loop to limit the amount of swing the bag can have as you move.