Possible contradiction between Ohm's Law, KCL, KVL and Faraday's Law of Induction?
This is essentially a long way of saying that KVL finds itself contradicted.

Kirchhoff's Voltage Law is a law from circuit theory that is valid in the lumped circuit approximation. One of the requirements for the lumped circuit approximation is that there be no significant changing magnetic flux passing through the circuit. If this requirement is violated then we absolutely don't expect KVL to apply.

What did I do wrong in all those steps?

When you said, &quot; since we start at any point in the loop and come back around to the same point, that means that the voltage at that point (relative to itself) is both 0 V (trivially) and ...&quot; you have already assumed that the lumped circuit approximation is valid and that there are no changing magnetic fluxes through the loop.
You assumed KVL would apply in a circuit where it doesn't apply.

Which assumption was incorrect?

The assumption that there was no magnetic flux through the circuit being evaluated

But I took this long way to avoid answers such as &quot;KVL simply doesn't work with magnetic fluxes&quot;.

You basically demonstrated the reason why KVL doesn't work in circuits with changing magnetic flux.
If you want a reason why KVL doesn't work in this scenario, then your logic is exactly that reason. It's because in this scenario the integral of the EMF around the loop is not zero but something that depends on the changing magnetic flux through the loop.
If you want to model this circuit within the context of the lumped circuit approximation and KVL, then you should treat each element of the loop not as a small resistor, but as a small section of the secondary of a transformer (with the primary being whatever is generating the magnetic flux through the loop). Then you have a term for the voltage across each element that won't sum to zero as you go around the loop and you won't get a contradiction.