Tim,
I haven't seen these items, so this is a guess. Loctite and a bazillion others make two part epoxy compounds...everyone here knows J-B Weld.
Would it be possible to clean the shaft and little spines of all old knob material and make it bright and clean.
Mix your 5-minute two part epoxy and stick a little gob into the hole on the new knob and shove it on. When it dries, it should be just-almost-like new.
Because I haven't done this, maybe I am over simplifying it.
Stuart