I did some searching around and found another source for replacement Predicta antenna rods - Zenith Chromantennas. Apologies to any Chromantenna fans.
Here are the patients with broken or missing rods.
Here's the inside of the Chromantenna.
I used a Dremel tool with cutoff wheel to carefully cut the plastic rod supports out. Then a sharp utility knife to trim off the support ribs around the cylinders.
The diameter is perfect, but they have a beveled shoulder while the originals are right angles. They will still work as is, but not fit quite as snuggly. I suppose they could be squared up with a file.
The newer plastic (mid 70s ?) is not as strong as the late 50s stuff but should hold up OK.
I should also point out that these will not collapse inside like the originals did. There will always but about a foot sticking out.