Here are a couple of variants I have used that I think work. One is for movement and the other is a way to play solo.
Movement: For movement the game originally uses a single die. This results in very slow play. So when my friends and I play we use two dice. And to really speed things up every time we roll doubles we view it as your player successfully hailing a cab and then moving to any place on the map.
The fun part of the game is getting the clues and deducing the answers. So speeding it up makes it much more entertaining. True, rolling dice like this still makes luck a factor but with enough rolls and enough games it will even out.
While I agree with you,(and many others as well who complain about the slow movement of using one die), I have found that when we use two dice, then we find ourselves waiting around to get a chance to see the clue book. Because of the quicker movement pace the game comes to halt, as a traffic jam occurs with two or three people waiting for their chance with the clue book. That is almost as frustrating as rolling a low number on a single die, thus taking longer to get to the location.