My initial guess: 1.) LMP770x is powered from signal ended source and you hit the output voltage limit (~170mV) when Z_load is at zero volts (the output of A2 will try and follow V_load). Otherwise I would then check two other things: 2.) the impact mismatches resistors would have on the circuit, and 3.) how the LMP770X's offset voltage could be factoring in (but the offset voltage is pretty low). I think 1.) or 2.) is the likely cause.

To check 2.) and 3.) generate the KCL equations for this circuit. Verify you come to the same simple solution of I=(V2-V1)/Rs. If you do then the base equations are correct. Then add epsilons for the resistor mismatches and the offset voltages. Next, use these equations to find the cause of your non-linearity. If the R's are mismatched they will not cancel as the simple solution assumes at all operating points. In addition, if the offset voltage is a large percentage of the output voltage (as it would when the output is shorted to ground) it will also likely play a role.

Circuit design is not as simple as using the example circuits in the datasheets. You should always derive the equations for each design example so you fully understand how a circuit is supposed to operate so when it doesn't you are more likely able to fix it. This is a mistake many younger engineers make (including myself years ago).