Using the heat analogy as I don't understand the electrickery stuff: it's been about 30 years since I last studied it. Thanks for explaining!
The problem is you're trying to fix both the value and the rate: one MUST float to allow the other to be true. Otherwise you are fixing the outer value, then the wall adjacent cell value, but to avoid problems the next cell is also fixed etc. The whole domain is then purely a function of the outer temperature and set gradient. Not the result of anything else that may or may not be happening. It's a common misconception. We set a flux in an experiment (or temperature) and measure the other, we can't set both: simulation is much same but in a computer.