This being a potential question for my own project, I looked at using the shaper – manually-operated in my case.
The text-books for that indicated internal shaping is by drawing the tool through the work, with the clapper-box locked. The latter point is emulated by using the lathe as a shaper by winding the saddle back and forth (not recommended for frequent use).
Though not explained, I think this is to avoid digging-in, as the spring of the tool-bar will tend to lift it. The top-rake should be low to minimise the risk further.
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The tool-bar is best not contacting the bore, as you don't want to risk scoring or wearing that. and anyway if made the same diameter would require either the flanks cutting back to allow down-feeding, or setting the feed by adjusting the tool-bit itself. The area ahead of the cutting edge needs enough relief to accommodate the shaving.
If needed, you can relieve the tool on both the shaper and lathe by using the appropriate feed-screw. (For short, one-off operations such relieving might not be necessary anyway.)
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To support a drill or slot-drill removing the bulk of the slot material, plug the bore with a piece of the same material.
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I don't know the gear-hobbing machine you describe so I don't know what are specified for the universal joints, but neat ball-type joints are commercially available, that would very likely handle the loads on this machine. I have set two aside for the feed-drive on a small horizontal mill I am slowly re-commissioning.