Try Olympic bunker, the next question would be " how to speed it up?"
In a serious note,"slowing down" is not the way and "thinking" to cut down from your reaction time is a non sense for a sport that relies on good eyes, reflexes and execution time.
" Thinking" that you have to slow down,just put an other concern on your back which you don't need!! Sometimes you will be too slow or too fast for a target that always flies away from you.
I would add, to the very good points on this thread, beside long call to eliminate the air from your lungs,to work on your gun holding point until you match your reaction( start) with the speed of the bird.
The bird needs to " tell" you how fast you have to move the gun and not you to tell yourself to "slow down" or "speed up"!
The only thing you have to learn, until becomes a routine, is to keep the gun still until the target passed your barrel.
Here comes in place the holding point,visual interception of the target and your reflexes! Smooth it doesn't mean " slow"