Sorry, perhaps the Support, as suggested, would have been the better way.
I have attached here an aep file with your cube and an adjusted cube.
Besides that, I know the main that counts is a product. So let me share two options:
a) use the RE:Vision UV Map to get the UV information into Ae and map the image on 2D layer, without all the trouble of axis stuff.
b) set your whole scene under a Null and use the Comp Tag with the Tag>Matt Object set to black, and render out only the images you need to swap out, should go very fast, the image-object has no Matt Object on, is seen by the camera. This gives you a very fast “Buffer” for this object. (BTW, This is normally used to shut everything off, and allow for up to 3 (RGB) or even 7 channels in an RGB image (r,g,b,rg,rb,bg,rgb, well you can have more, if you key)
With the same setting, you can render an image only for the object that would hold the image, and everything else is off. The reflections for teh images and light impressions need to be rendered before. The rendering of the images should go very fast while there are only in the luminance-channel.
I prefer to stay in C4D as long as possible. Right, that is an workflow / pipeline discussion.
All the best
Sassi
