Sir Terry. . . . .

Gadzooks no, dont give up on that tuning knob. the broken piece shown at the very front and its area just behind, should fit back into place to then let you measure that critical height dimension . . . from the flat base of the back of the knob up to the tip
of that broken shaft shard.

From what I can make out of the remaining knob shaft internals, I dont think that I see any longitudinal spline markings within the
knob shaft.

Also it does not seem to be a half round shaft.

One other shaft configuration coming to mind is a round shaft which has flats coming down ~ 25% inwardly to the center of the shaft from its top and bottom.

At any rate the final bit of info needed to be acquired is its manner of indexing the knob to the shaft such that the knob calibration of its markings will be retained.

As for the use of a round shaft and relying upon that strong compression spring, don't think that would be the case ,with the same knob being used for the tuning, any forcing of it at the end of its travel would cause it to further rotate and throw dial calibration off.

As mentioned, with the indexing info, and the height of the shaft fron the base of the knob should permit the cutting off of the frontal
porton of a like knob and using its shaft after trimmed to length and then the affixing to the back of the original knob with epoxy putty.

After the old knob shaft remnants have been reduced to a flat area on the back of the knob, rough up that area to enhance cohesion.

Measure the diameter of the shaft, take a compass and adjust its arc to be able to place the pivot point at the edge of the knob and then inwardly transcribe (4) 90 degree separated arcs on the knob back. That then lets you sight against those marks in preciseley centering the shaft positioning while bonding it to the back of the knob. An eccentric tuning knob would be intolerable.

I think that in seeing that knob shard , that knob just might have a thin mylar style of metal covering over it. Not chrome, not gold, but a subtle shade of both of those colors. An Exacto knife blade to a portion should reveal it as having a thin metallic overcoating, excluding the round white path circling the knob shaft, as seen on the shard that had the knob spring riding atop and covering that non metallized area.

Some how in the heating and chemical processing involved with that type of knob construction, they end up brittle , as compared to a common knob..

Many are the times I have seen that "metallized" type of knob on a television, looking like it is a chrome or gold solid metal knob.
In hard rotational service, like a channel selector, they crash just as yours has done.

If your shaft configuration happens to be the round unit with 1/4 flats inward from top and bottom, a solution for that might be a full service hardware store and getting an aluminum collar of 3/4 in outer diameter by a proper height . .or to be reduced to the required height.

With the unit having a 1/4 in center hole, such as a collar does. Then the collars side portion is tapped for a set screw to lock and index the knob to the tuning condenser shaft.

Keep on plugging !