Bob bob wrote:
"The low level thinking (for me) on a transmission line is that for a
pair of wires, the signal on one side is always 180 degrees out of phase
with the other."

That follows for me from the action of the simplest phase inverter, the
center-tapped coil. Feed one end against the center. The other end is
out-of-phase.

The current in opposite wires of a transmission line is flowing in
opposite directions. Hence, the wires are out of phase.

I think a parallel-wire transmission line has a self-balancing tendency.

Two parallel wires form the simplest transmission line, with the power
source at one end and a load at the other.

Distributed along the wires are series resistance, series inductance,
shunt capacitance, and shunt conductance.

Power travels from the source toward the load in the incident wave.
Velocity of the wave and voltage to current ratio in the wires depend on
construction of the line.

The destributed inductance in one parallel wire couples with its mate to
form a mutual reactance. The two wires are inductively coupled. They`re
also capacitively coupled.

With inductive coupling, Lenz`s law says, "the induced current is in
such direction that it opposes the change that produced it". It`s
reactive, pushing back at the imposed current. It flows in the opposite
direction. This is evident in self induction and secondary currents.
Induced current is out of phase.

With current in one wire inducing our of phase current in the opposite
wire of a long transmission line of closely coupled wires, balance
between the wires is enhanced.

Best regards, Richard Harrison, KB5WZI