One of the jobs of the pivot pin is to keep the handle (tang forks) tight against the blade so that the handles will swing in a straight arc. However, Jaguars are known to have bad pivot pins installed from the factory.
Based on what you've described, the existing pins are compressing within itself between the two "heads" and then gets stretched out again when you play. Ideally, you should be removing the excess pivot pin by mushrooming the heads a little more, and thus shortening the length from the ends, not the middles. Try hammering again with 2 old and dull razor blades in between the handle and the blade. This will help remove the slack, and force the pivot pin to compress at the ends. Repeat the process with one of the razor blades removed, and finally again with no razor blades.
If that fails, it may be time to replace the pin. Use the link in the first response for that process.
Hope this helps and good luck.