Last night measurements didn't work well: even without exciting the modes, the ADC was saturating because of the low frequency signal, particularly a 58 Hz peak:
When the modes were rang up, thing got clearly even worse:
So I modified the whitening filter, changing C6 from 2.2u to 220nF. The old and new whitening filters are shown below. We have the same amount of whitening at high frequency, but less amplification of the junk at ~50-100 Hz
With this modification, there's no more saturation, even when the modes are excited.