Electrical – How does the diode clamper circuit clamp

Your description sounds exactly like a full wave bridge rectifier.

A multimeter in diode mode usually displays the voltage drop measured across the diode under test, as a small current is passed through it.

A single silicon diode usually has a forward bias voltage drop around 0.7V, so your reading of 500 to 700 probably corresponds to 500 to 700 milivolts.

When you measure across the AC input, you'll be measuring 2 diodes in series, plus the series resistance of the motor winding. Your measurement of 1200 to 1400 mV still makes perfect sense.

I wouldn't bother with the analog amplification or the RC filter to DC part. Just turn the AC into full wave rectified DC. I assume that if you have a ADC and an EEPROM that you're using a uController. If so, create a simple peak check algorithm (if current value is less than previous value within time frame, then you're at peak). You could take the last 5-10 or whatever peaks that you've found and average them to get a more precise measurement.

Amplification and level shifting you're trying to accomplish with op-amps will introduce offset errors and multiplication errors, so you won't gain any accuracy. Just use the 1.3 to 2.2 V signal you have now directly into the ADC.

FiddyOhm makes a good point. If you want to full-wave rectify this, you'll gain a lot more accuracy at the low end by using lower voltage drop Schottky diodes.