I tried to subtract the 60 Hz AC noise from h(t), by an unused ADC channel + bandpass filter (59.6 - 60.4 Hz) + time shift (-0.069 s) + scale (2e-18) .

Fig.1 top : ASDs for the strain (blue), subtruction (orange), and subtructed (green) signals.
Fig.1 bottom : coherence between the unused ADC channel and original (blue) / subtructed (green) strain.
Fig. 2 : 59-61 Hz band passed timeseries for  for the strain (blue), subtruction (orange), and subtructed (green) signals.

It looks working well.