Yeah, that much of the solution was obvious, but I still have no idea how. Pushing a box into a cart doesn't do it. Crushing a box between carts doesn't do it. The box doesn't push carts, so I can't push one into a wall. There isn't a convenient turn-right-before-a-wall implied by the architecture to let me push a box into the way of a turn after the train has passed, though I think I can see how to make that not necessary now.
(I never saw the point of the fourth of the three hollow cubes, by the way. Not sure what the 'easy' path was.)