Electronic – Op amp output voltage offset too high

First, the DUT is in the positive feedback because this way you have an inverting and a non-inverting gain in the loop, so that multiplying them you obtain an overall negative loop gain.

Second, the gain is 1000 because Vin of DUT is Vos*50/(50K+50), so if you consider that V+ of the DUT should be 0, there is only the offset applied, so the feedback forces the output to be 1k times the offset voltage.

I think that you can look at the output this way: suppose that the situation is the one described, and you have a 500uV DUT offset and so 500mV output voltage.

Now, if you try to perturb the Servo Input, the feedback forces the output of the DUT to be almost the same of Servo Input, restoring the same Output voltage.

Note: Voff is the conventional name for input offset voltage, while Vos is the output voltage with Voff applied at the input pins.

Im curious why you are using aplification. In my opinion simple cell voltage measuerement could look just like this (i drawed it only for 3 cells):

This should give you acurracy probably below 0.5% + resistor tolerance, but you can compensate resistor tolerance in software.

This is how very acurrate cell measurement can be done

This is part of cell voltage measurement circuit from well designed 6 cell battery charger:

You can find full version of this schematic here

LM324 amplifiers were used in very good Turnigy Accucell 6 and some other RC battery chargers in cell balancer circuits.