It's very useful too being able to transfer the chuck with the work still in it, to the mill or bench-drill. I have a Warco dividing-head that accepts Myford chucks, and made an adaptor to hold a Myford nose-piece on the jig-borer (though at some loss of the already limited headroom).
For parting-off though I prefer to cut partially to depth first, to a shade below what will be the floors on such features as flats or scalloping. This gives the parting-tool a continuous surface both starting and completing the operation.
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I have used the hole in a block of wood trick successfully, but would make a spindle plug reasonably long (1 – 2 inches): a semi-rigid plastic like Nylon or PVC, or even hardwood, would be fine. If you envisage a lot of work using long stock it may be worth fitting a tube on a stand behind the headstock, to support and enclose the bar completely. Even then a support-plug at the bar end as well as spindle would be a wise idea, but consider how to deal with the seam if you use ERW steel tube.
Such a stand was a standard accessory for capstan lathes. The tube could be swung outwards at the lathe end for loading, and for a capstan was also fitted with a bar-feeder that pushed the material up a to stop set as one of the tailstock tools.