I know what is wrong witht he model, the ink from the printer is making the paper bend and change shape, and this will happen when the paper that the model is been built out of is to thin and the paper the will change it's shape.
Going to thicker paper will help but maybe setting to printer to use less ink and also putting the paper in a press to force it back into a flat shape should also help.
Looking at the model it looks like one for the bucket list for me, I am now busy thinking of what to build next after my massive project is complete and I think this may be it.
R