Heh, I had a feeling I should. No worries 
Yeah, I was really hoping not to have to rehash this tester again. But, as 4-terminal testing has already been suggested, I suppose there is no way around it.
That is probably the easiest point to break the chain at. These wires are soldered into a daughter board (which the resistors are mounted to), so unsoldering them shouldn't be much of a challenge.
Connect these to 2 analog inputs you mean? I.e. A0 and A1 will be hooked to MV1 and MV2, and then A2+ will be connected to each subsequence resistor network as it is currently? If so, I'll need to find a way to multiplex then. All 16 analog inputs are currently being used with the current setup.
My current bus bar is quite robust as it is and is soldered directly to the PSU. It's only the wire leading into the resistor networks that are thin.
Of note, this morning, I have rewired the board to only use the master PSU (the 5.15V @ 10A powering the rails). Everything, including the Arduino, is running off this single PSU. Under full load, I am seeing the resistor networks consume, at most, 4-5A with no drop in the voltage from the PSU. I've seen marginal improvement to where I am now barely within my goal of +/- 0.5 ohms. But, I would still like to see this improve if at all possible.