Nathan
Here is my personal opinion about the proper way to turn the razor on the strop.
Two barbers back in the 1960's told me that I should strop with my thumb on top of the tang. And some wrist turning is OK.
They also told me that if I wrap my little finger and my ring finger lightly around the handle, it would help me turn [manipulate] the razor with very little wrist turning. Those two fingers on the handle give me more control when changing direction on the strop. It works quite well for me all these years.
Also you must keep the spine in contact with the strop at all times and practice stropping in slow motion until you feel confident with your stropping method. Strop slow enough so you can actually see the edge flipping at the correct moment.
I just thought I would tell you what the barbers told me.
Examine this thought. On each stroke you are making a 180 degree change of direction. Do not start this change of direction until you have lifted the cutting edge off of the strop and do not let the edge touch the strop until you have fully changed direction.
You must come to a complete stop before you can change direction. During this momentary "stop", the razor edge should not be touching the strop. The edge only goes back on the strop when the directional change is completed and your hand and razor edge is moving in the correct direction.
Practice all of the above in absolute slow motion and try to see and feel the edge come off the strop at the right moment and go back on the strop at the right moment.
Focus on keeping the razor flat on the strop just as if you were on a stone hone.
The edge only belongs on the strop when it is moving in the right direction.
Again, do all this in SLOW MOTION until you can feel the correct stropping stroke. I always take a deep breath first and always start with the "toward me" stroke.
Stropping is a matter of precise timing just like a musician counting time while playing an instrument. You need to be your own personal judge and you need to be tough on yourself.
S L O W M O T I O N and counting are the keys to developing a successful stropping stroke. There is no reason to nick a strop if you have a rythmic system and you are properly focused.
Good luck.............Jerry