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Yes John a mil could be substituted for the lathe, but you are still stuck finding the correct and\gle and offset in order to drill a matching hole in the hand wheel collar so the taper pin fits both the shaft and the collar without drilling another hole in the shaft.
Of course drilling a second hole is always an option.
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I may be walking into it here, but I have to ask: If a vertical miller is available, couldn’t the hand wheel shaft be loosely fitted into a vise with a vee block, a drill suitable to the shaft hole, held in the headstock, and the shaft and drill manipulated until there is a “free feel" to the drill? Perhaps a tapered reamer could be “jiggled” to assure alignments afterward. This might be as sensitive as trying to fit a level in Jim’s procedure. I would proceed as Jim has suggested, using super glue, spotting center, and drilling very cautiously. Not as easily, I suspect the same thing could be done with an horizontal miller. (Lucky me: I have both.)
I am probably missing some important point, so have at it. I am not sensitive to being corrected.