To copy Batting Order: If you first select any game and then add a new game, the batting order is used from the selected game.
To Copy all other data, including positions, you simple create a Duplicate of the game (Reports -> Duplicate Reports menu item). To keep only positions, you would zero out/clear the other statistics.
You can quickly to this by entering 0's or blanks in the top row and then entering into "Selection Mode" (Edit -> Selection Mode menu item). Drag to select all the top row and then choose the Edit -> Fill Down menu item.