After numerous tests, we concluded that we can no longer use the high frequency mode on the welder. It created too many problems. First of all, it produced too much electrical noise (even though we are using shielded wires). It gave our foundry a mind of its own! Once during a test, the foundry started doing weird things when the high frequency turned on. Weird things, as in moving the electrode up and down while pouring without even being commanded to! Second of all, the welder somehow knew our circuit was connected to it. The welder had problems starting an arc each time we were trying our circuit.
So, back to the drawing board! We studied the welder and found another place we can measure voltage with the high frequency disabled. We created a simpler circuit, as shown below, that uses a single op-amp instead of two.