A lot of commercial antennas are built like that, but performance suffers as the velocity
factor of the half wave sections decreases below 1.0 because of the difference between
the current distribution inside the coax (where the velocity factor applies) and the current
flowing on the outside of the shields that is responsible for radiation (where the velocity
factor would be different.)
Commercial designs use copper pipe and wire with various sorts of spacers to make coaxial
lines with a velocity factor very close to 1.0 instead of coax cable sections.
First, is there any reason why I can’t place the ¼ wave aluminum/copper sleeve balun inside the PVC or fiberglass rod with the ferrite beads below, and a female N-type connector below that?
That should work.
I plan to mount the connector to an aluminum plate so I can attach the ¼ radials. (I'm only going to use 4 half-wave dipoles to keep the antenna length shorter.)
Why are you adding radials?