The momentum of the piston is completely irrelevant to this problem. Also, simply picking up an object moving in the same direction as you does not mean you changed its entire motion vector, most of its motion vector remained the same. Also, to further clarify the irrelevance of the portals or piston momentum. Replace the cube with a 10 mile long rod. Ten miles of rod comes out the blue portal, then stops dead? Why. How does the universe even decide what atoms are part of the rod and should stop.