I plan to do some characterization of this problem. The plan is to use THD as a metric for whether we are having hidden saturations. Pg 9 of the LT1125 datasheet tells us what fraction of THD to expect. I will use one of the several unused DAC channels available at the LSC rack to drive a 100Hz sine wave into one of the inputs of the whitening chassis, and measure the THD up to a reasonable harmonic number (will probably be set by the ADC noise) for (i) various whitening gain settings and (ii) various input signal amplitudes.
The motivation is to attempt to quantify the problem better:
Then we can decide what, if anything, to do about this issue.