I’ve finally managed to fix the problem by deciding to bite the bullet and re-animating the swing animation. The new animation is almost twice as long as the old one, although I had to go back a second time and shorten the animation by four frames to get it to properly work with the Animation Notify. I guess the animation can’t be too short or too long in order for the Notify to function correctly.
Anyways, everything now seems to be in more-or-less working order, so thanks for all the help!