A different charger perhaps? The resistor idea has not much chance of success. And... is anything getting warm/hot? Catching up here and interrupted, I now see you tried a good PSU.
You asked about the power routing on board. Different Arduinos have different arrangements for the negotiation of power from the jack and from the USB plug. There is always a need to do that, so for example the jack power won't run into and destroy the computer USB port. Some are very simple, like the single diode on the Nano. Uno and Mega, better at least I think i remember seeing some MOSFET circuit there to drop the least voltage while switching power.
So although a lot of ideas could be put together, they might never get to the heart of it. First and foremost, you really need to test the shield and Arduino separately.