I just cant see how eithet takes away choice. If the players can go north or west to get to the next mcguffin. I would put an encounter on their road either rolled or desined. After all it is common in d&d to have road battles. The battle will be on what road they chose. I would make the encounter make sense and based on the pc.
If we down scale this to a dungeon so it 3 rooms not roads. What changes?