In addition to the air variable capacitors, three of the parts bins contained a bunch of pre-wound antenna coils, including these that looked unused. One of them even had an instruction sheet.
Calrad CLS Loopstick.
They consist of two coils, one wound on top of the other and what seems to be a ferrite rod inside that can be tuned by turning the screwdriver or even a knob at the other end.
One was also in a box, a Miller A-5495-A with two separate coils and a capacitor. Looks like it has a tuning range of 540 - 1700 kHz, which is the AM broadcast band.
This one was tunable as well by turning the screw at the end.
Now, if I can find some Ge diodes, I wonder if I could use these in a crystal radio...