Rather than 3d printing larger boards, why not create a piece that will allow a ball to travel from one board to another? That way you could link multiple Turing Tumble sets together to create larger machines.
edit: Alternatively, the equivalent could be achieved by making the sides/top/bottom removable.
Example: to join two boards vertically: remove top from lower board, and bottom from upper board.
To join two boards side-by-side: remove right side of left board and left side of right board.