SOLVED! So, the problem was that I had the collision shape in the animation player.
To specify, this was the shape itself, and not the shape:size.
Once that was removed and the collision box was set to local_to_scene, the two character instances stop sharing the same collision shape frame by frame.
Shoutout to "Balthamel 9♦" and "Nisovin" on the Discord community server. Would not have figured it out on my own.