1. Ferrite and powdered iron are entirely different materials, with
different physical and magnetic characteristics. Powdered iron isn't a
good choice for this application.

Powdered iron should work better because of the higher permeability even
under heavy load in comparision to ferrite. I think so in theory - not
tested.

2. You're not likely to drive either one into a nonlinear region when
they're in the form of a rod because of the large air gap in the
magnetic path.

Can you explain this more detailed Ron? What will happen with the air gap?
The losses in the air gap radiates and that is the antenna function?

- Henry