The only other thing I'm seeing so far is a pretty high bias (hundreds of q) on each channel. Enabling common mode servo only changes the bias by single digit values. The RMS value of the input noise looks reasonable in magnitude if somewhat imbalanced (4q on one channel, 8q on the other).
My input circuit is based on figure 3 from the evaluation module manual. The resistors between VCM injection point and +/- inputs are 1% tolerance, and I measure 0.000V across the inputs on both channels.