Seamless Cubemap Generation to Map on Quadcube

I have a quadcube generated from a cube that I want to texture. Six textures are generated randomly. If I mapped them directly onto the quadcube, they would look very distorted, so I distort them beforehand using pincushion distortion so the distortions cancel each other out. The problem is that by pre-distorting the texture, parts of it are being cut off so very ugly seams occur.

How could I modify the texture generation to achieve seamless transitions between the six textures? Or do I do it all wrong?

Because I cannot post more than two links in one question, here is a gallery containing some images of my problem.

I'm thankful for every kind of help. Thanks.