Firstly, do not use diodes. These are non linear devices and cannot be used to accurately drop voltage.
Why do you need to scale via an opamp, other than adding complication to what could be an extremely simple circuit.
With 1000:1 resolution (10bit) over the 5 volt span, an effective range of 2.5 to 5 volts will give you a 500:1 resolution of your 0-80 amps. Isn't this not good enough for your purpose. After all, if it was an analogue meter, could you really read 1/500 of scale.
Added to the argument is the question of what will you use to calibrate your 1000:1 circuit (0.1%). Most of us work with cheap DVMs which at best are +-1%.
You set your software to set 2.5 volts as 0 amps and 5 volts as +80 amps, with an effective resolution of around 160ma. No calibration required !
jack