Inconsistent vertex count between keyframes that have same number of vertices

Hello, I'm having a frustrating issue that I'm honestly at wit's end trying to solve. I have a path with keyframes on it. Each keyframe has 12 vertices. But for some reason AE is still interpolating the path by creating and deleting vertices between the keyframes. Essentially, it is creating a new vertex at a random place in the path, and thenit deletes another vertex. So it starts and ends with 12, but between those keyframes there are 13 vertices.

The reason this is annoying? Not only does it look janky, but I'm trying to put a joystick on it using the joysticks n sliders plugin, but the plugin requires that all paths bound to a joystick have the same number of vertices at all times, so when I try to bind, it yields an error.

My "Preserve constant vertex point count when editing masks" setting is checked in my general preferences. I tried unchecking it to see if it changed anything, but it did not.