Would it be possible to rebuild one using 3d printed parts (probably laser sintered metal would be the best)... And then, build an analytical engine... And then make the analytical engine drive a 3d printer...
As the difference engine computes result of polynomial equations (upto x to the power 7, if I remember the demo correctly) , I don't think its turing complete enough to drive a 3d-printer completely. It can, perhaps, drive the generative design of a 3d printed art based on the result of a polynomial equation.