In the tetrahedral scenario what you basically have is a Wheatstone bridge that has 4 resistors, and a resistor across the Up/Down (UD) and another resistor across left/right (LR). The shape matters little.
As usual, if all bridge resistors (ignore the top/down TD and left/right LR resistors) are equal - and you apply a voltage across the top/down there will not be a voltage across the LR resistor since the bridge is balanced.
Measure all options 12, 13, 23... Figure out which has the lowest -imbalance. The Top/Down resistor is the culprit for the imbalance in the other options. Fix it, redo the testing.
I don't believe that mOhms to nanoOhms can be done by filing the junction mOhms yes. uOhms - Ehhh. nOhms? No way...
Maybe they drill fine holes, tap them, and insert a screw into the tetrajunction. By adjusting the screw "depth" the resistivity will change ever so slightly. The smaller the screw, the finer the resolution... Then goop it as a fancy "do not touch" warning...
Or parallel a few gigohm resistors in parallel to your thick tetrajunction arms.
(that would be amazing - a 0ohm in parallel with a glass embedded mega to multi GOhm resistor - talk about wasting money...).
Hmmmm - this process should also work for your tetrajunction.
So let's theorize a process:
1. Figure out which pair has the highest imbalance (say force 1-2 measure 3-4 results in the highest NV reading).
2. So your highest imbalance is either 1-3 2-3 1-4 or 2-4. (the imbalance is always in the bridge - not the resistors across TD or LR).
3. You can deduce the pair by the polarity. So if the 3 is positive (to 4) the offending "resistors" are either 1-3 or 2-4. Feed 1-3 (and measure 2-4) and Feed 2-4 (and measure 1-3). Whomever has the lowest imbalance - assuming feeding 1-3 results in a lower voltage across 2-4 - means resistor 1-3 needs to be lowered somewhat. Solder a resistor across 1-3. Repeat.
(Note: I am a bit on the fence about how to relate the imbalance nano volts to gigohm resistors, though.... Should be simple wheatstone bridge analysis, but having a superposition of 6 of these makes my head spin. The symmetry reeks of a simpler way to solve the equations...)
4. Perhaps one doesn't need a trick. Solder a resistor across 1-3. Measure 1-3 and 2-4 again. Decrease the value of the resistor until measurements 1-3 and 2-4 balance out. Repeat the entire exercise. Do this until all 4 balance out.
Note: The resistors need to be soldered where the wires connect to the tetrajunction. Not to the tetrajunction itself, though, as heating it will change its properties. A solder lug under the screw perhaps?