Animated textures for facial expressions

So I made a character in the semi-low poly style of the new Animal Crossing game. I really like how it turned out. However, I want to use textures to animate the eyes and mouth. Furthermore, his current face was done in texture paint as a mixture of just painting it as well as using a stencil for the eyes, and I want to be able to keep it if possible.

I figured to animate textures, I’d simply have that amongst other expressions on their own texture and simply change the coordinates when animating. However, UVs are a nasty beast and I’m not sure how to approach that aforementioned way. I tried scaling the UVs along X and Y to straight lines, but that just messes things up. What’s more, if I paint one expression, there doesn’t seem any way of using a previous one as a guide for the next one, and as such, the eyes or mouth might jitter around. I think there might be a way in texture paint mode of painting on the UVs instead of the model in some cases, but I’m not sure.