On Sun, 5 May 2019 08:21:19 -0500, dpb wrote:

On 5/5/2019 7:49 AM, dpb wrote:
...

There's somewhat under an inch left past the face plate; it has to have
sufficient clearance to be pushed inward by about a 1/4-3/8 inch to
engage the clock-setting function; so the knob can't use up the whole
length--hence the wish to extend the shaft somewhat again...the broken
pieces are roughly 5/8" in length...
...

The above I see is somewhat misleading -- that's to the face of the
clock face itself, not the covering face...there's only about 1/4" or
less past the outer cover.
So you need something with a bore of 1/8 inch about half an inch deep
- about an inch and an eighth long? How far past the end of the shaft
did the knob extend? What diameter is/was the knob?. How big can it be
where it passes through the plastic face plate?