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I guess it depends how you define 'direction'.
I start by going 'from the inside, over the top to the outside' ie anticlockwise on the left, clockwise on the right, which is (I think) generally regarded as the way to do it to avoid it unwrapping as you ride. It certainly works for me.
With tape like the Cinelli stuff that has 'directional' branding I'll have to find the right end of each roll to start from to make sure the branding is visible and wrapping my way keeps it visible up top and I've never had any problems with it unwrapping or loosening going 'up at the back, over the top and to the front' on the tops.
You're suggesting the tops should really go 'up at the front, over the top and to the back'?
Thanks for the late night ramblings, I'm also still here! I was scratching my head trying to figure out your first post, pictures help a lot.
I will give it a try next time I need to wrap some bars, alas I am noticing two things : it is definitely bulkier than my method, and the bartape on the tops seems to wind up in the wrong direction if I'm understanding your pictures correctly.