If you treat the op amp + R4 as a transimpedance amp
then its closed loop transimpedance is 1K and your
20mA input crest current should make a -20V output,
well greater than the +/-12V op amps can follow. To
this you are also adding 10mA from the VREF (which
would at crest drive you to -30V). What you probably
are seeing, is that only the lowest currents can be
amplified without clipping in the first stage, and the
clipped signal can't be restored by the second stage
offset.
Lower DAC current, or constrain first stage to remain
linear with max DAC current, and make it up in the
second stage?