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I'm not sure that's what he meant. I read it as he is hooking it by the handle end, & holding it by the hook end. The result being that he's still stropping on the same side, just starting the stroke...

I can't see you doing any harm by that. There are only so many strops whose design will allow you to do that, so i can't see it being common practice. Odd that it has increased the draw.