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I have hardwood dowels I turned for the various size bores that afford a tight fit,force the handle onto the dowel,sand and polish the bottom.
Many ways to do it.
I have used the dowel system myself Gerritt showed me how at one of the Yakima meets.. It is very safe and very solid... I have a set of small jaws that work also by expanding from inside the hole, but sometimes I think the dowels are safer...