Please ignore that its just wrong.
So the current flowing in all the resistor chains is all flowing through the thin supply wires (aka resistors). While I'm not saying its impossible my meories of working with Kirchoffs laws, Thevenin & Norton Thms are not up to working that one out.
There will be an (basically unknown) voltage drop across the ground, which you would need to compensate; and ALSO a voltage drop across the 5V supply that would change the reference voltage for your measurements.
Realistically you need to find a way to change the hardware to allow you to make a 4 terminal measurement.
Here is a suggestion. If you can break the connection between one of the resistor chains you can access the voltages you need to measure like this
Rw1, Rw2 represent the connecting wires;
As "no" current is drawn by the arduino analog inputs you can connect MV1, MV2 and measure voltage V1, V2.
Alternatively you could use MV1 as arduino ground and MV2 as arduino supply, so taking fewer analog inputs.
Or if you cant have seperate grounds you can use the voltage drop across RW2 to estimate that across RW1.
Of course these approaches will ONLY be accurate if the "bus bar" connections shown thicker in the diagram are relatively low resistance.