Turns out that was the problem. Thank you! My logic for pinning the two together is just "System -> Every Tick -> Player (the collision-less animations) -> Set Position to Base.X, Base.Y"
So I guess off the top of my head there are two ways to fix it. I'm assuming one is changing the last step to "Base.X-??, Base.Y-??" and just jimmy it until it looks right. The second would be to ditch the mask-base separation and give the player sprite all the collisions. However, something I plan to attempt to implement pretty soon is combat and the player's disjointed hitboxes. Since he's got a flag to attack, his flag swing should not occupy the same area as his body, so I was told I would need the mask-base separation to make two separate collision polygons, one for terrain collision/hurtboxes and the other for hitboxes. Is this true or do you know if there is an easier way to create a hitboxes-hurtboxes separation that would allow me to ditch the mask-base separation, provided ditching the mask-base is the best option?