The zone system allows you to pass without looking. Here's a few things to think about to get the ball down field. First, you can fake to pass or drive in one direction, get the defenders to move one way then pass or drive in another. Many players use this method very successfully. Think about the nature of the game when passing, driving or in any other facet of play.
All players hold the stick right handed.
A defender will face you with their stick pointing to the left. This will work especially well if your teammates are all on the same page about this. If they know the ball will be passed to the right side of the defender they can get into position to receive it better. Sometimes, especially in field hockey, thinking out some simple things like this can give you an advantage over teams that rely solely upon athleticism. A smart team with average skills can compete with teams that rely upon their superior athleticism only.