Voltage on a Transmission Line with Ideal Conductors
Remember that when we defined the electrostatic potential difference (aka "voltage"),

$$V=-\int \vec{E}\cdot d\vec\ell,$$

we called it the electrostatic potential difference because it is only strictly valid in electrostatics. When we use this concept in AC circuits, we're using it as an approximation only (usually described as the lumped circuit approximation). In particular, in the presence of time-varying magnetic fields, we can't count on this \$V\$ to be independent of the path over which we take the integral.

In transmission lines, we are definitely dealing with time-varying magnetic fields, so we can't expect the electrostatic potential difference to be well defined.

We define an approximate potential at a point along the transmission line as the negative integral of the electric field from one conductor to the other at that point. 

But we can't expect to get the same result (because this isn't an electrostatics situation) if we take an integral from some point on the first conductor, lengthwise along the conductor (with contribution 0, because the material is p.e.c.), across the gap at another location, and then back along the second conductor (again contributing 0) to the point opposite where we started. 

Meaning, if we take the integral to calculate the "voltage" across the transmission line at position \$z=0\$, we can't expect this integral to be the same at \$z=z_1\$ just because there's no electric field within the conductors.