So far we have put a lot of work into decoding the border of the original FEZ images numerically - there was clearly a cyclic pattern in the data but it wasn't completely obvious what it was. Instead of filtering out the border as black/white and assigning them values, why not filter out the letters graphically and see where that goes? I started with @Moritz Walter's original images and removed the FEZ shapes from the border. The center image shows the letter-shapes that had white borders removed. The right image shows all letter-shapes removed.
The border definitely has a repeating pattern in it. In fact, we're already familiar with this pattern:
If we scale the tiny XOR mask image up it looks like this:
That looks like the repeating border pattern in the original FEZ graphic!? Could this be an artifact of the original XORing of the image or something intentional?
You'll also notice the repeating pattern is only 8 squares in width whereas the tiny XOR image is 12. There isn't a perfect overlap and 4 columns are unused.
I did check graphically and the pattern in the "tall" image above does overlap exactly with the tiny XOR image...unfortunately there doesn't seem to be any new data in the image since we already have any data contained in this pattern from the mask image...