Roy, W7EL wrote:
"Can we make a physically small "phase reversing coil" that has 180
degree phase shift between its ends? If so, how?"

Yes. Kraus was discussing collinear arrays composed of 1/2-wave elements
interconnected by phase inverters to keep the currents in all elements
in-phase, that is, flowing in the same direction.

More than the phase delay of the coil is involved. Its self-capacitance
is involved in making a parallel resonant circuit at the operating
frequency.

The phase relations would be the same for a smaller inductance shunted
with a larger capacitance.

Two reasons for using self resonance; simplicity and wider bandwidth
with the low-C circuit.

These parallel resonant circuits replace short-circuit 1/4-wave stubs in
some collinears.

Best regards, Richard Harrison, KB5WZI