Can someone help provide me with an argument why the electric field
must be zero in a perfect conductor?
It's not clear exactly what you're looking for. In a sense, any argument attempting to prove that the electric field must be zero in a perfect conductor will beg the question.
For example, here's an excerpt from "Electromagnetics for High-Speed Analog and Digital Communication Circuits":
We could in fact define a perfect conductor as a material with zero
electric field inside the material. This is an alternative way to
define a perfect conductor without making any assumptions about
From this starting point, one reasons that
(1) if there's an electric field inside, it's not a perfect conductor
(2) if the material has a finite conductivity and there is a steady current through, there is an electric field inside proportional to the current density
(3) thus, if the material has finite conductivity, it's not a perfect conductor
Again, it's not clear to me precisely what you're looking for. If the above fails to address your question, please update and clarify your question.