If you've got your shaft coming from the 13mm end then the bottom will not be supported on the shaft so the tool will in theory only be in contact with a very small area of the shaft, assuming it's a taper from 13 to 13.3mm?

To me the only way to do it is as they have done it, i.e. push the shaft in from the bottom and a nut on the top to seat the tool.

Unless you have some sort of reverse collet where the bottom of the shaft is slotted and a tapered hole bored and tapped at the end so when you tighten it in it splayes the bottom to grip the tool? Hard to explain properly without a sketch...

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