Converting S parameters to Z parameters - divergence
You didn't mess up.

\$Z_{11}\$ is the input impedance when the other port is terminated with an open circuit.

Since your device is just a bit of wire, it has infinite input impedance when the other end is not connected to anything, and thus infinite \$Z_{11}\$.

This is an example of why we need different two port representations (S-parameters, Y-parameters, Z-parameters, H-parameters). There's certain devices that can't be represented in any particular representation.