Broken tenon

[Lostmason]

It is just a push in. I am confident I can remove the broken tenon from the mortise with a screw, like you said, or I have a screw extractor tool I can use. I would need to be careful that I don't crack or otherwise break the shank while doing so.
Any recommendations as where to order a replacement bit?

I would try the foreverstems they have several that would compliment that bowl nicely. That is if you find one that fits or is just a hair oversize and you can sand it down.

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Doesn't look like you need a new one. I'd just fix the one you have with a delrin insert.

Where can I find the delrin insert?

edit: Googeled it,looks like one could pick up a small brass insert from lowes or home depot