They all share the same +5 power source and they all share the same data line to the Arduino.
That would be nice, but in this case after the first cell the voltages are too high.
Somehow, I don't think this is going to be easy.
Not as easy as you would like I'm sure.
I'm hoping that anything I can come up with, can be used with those existing wires
My 45-processor idea is designed to reduce wiring and it could still use those wires, however in this case the wires are already in place so probably using relays would be better.
What you need to do is the automatic equivalent of the manual method you are currently employing. Using relays (or maybe MUXs) you "walk" two connections along the 45 batteries taking readings as you go. This means that, like your hand-held meter the Arduino has to be floating and not powered from the same source or connected to the same ground.
Rob