Pjcamper, welcome to the forum. First you don't have to be fully stopped to reverse direction. When I want to reverse, I simultaneously pull the appropriate handle and move the fins back and forth in short strokes. You can feel the fins reversing as you do this. Once this is complete, the fins will lock in place by simply moving back and forth and you can release the handle.
There are a couple of things that can be causing your click. You will notice that your fins should have a small amount of freedom of movement at the back of the fin attaches to the "boom". As they swing back and forth in this slot ("traveler"), you can sometimes feel them hitting the stop. If the fin is adjusted too tight, it will tend to jamb in the treveler and suddenly break free and hit the limit. This may be the source of your clunk. The proper adjustment is to turn the wheel so that the fins can slide up and down along the "mast" about 1/8 inch. This prevents binding in the traveler and is the most efficient setting for the fins. After making this adjustment, the clicking sound may or may not go away but you'll get the best performance for your effort!
Here is a picture of the traveler.
