I looked at Jennie's and Camilla's spot position test (76770) to check if the movements had an effect on the sensitivity. In brief: yes, they do.
The largest effect is at low frequency (<30 Hz, see spectra and ratio to nominal values) and most evident with CAM_YAW2_OFFSET, and to a smaller extent with CAM_PIT2_OFFSET. Those changes are probably what was driving the change in range: I believe they're due to the fact tha by changing the spot position one changes the optimal A2L coefficients that are used on ITMY to minimize the coupling of CHARD and DHARD. So my guess is that one should ignore those changes since they are likely recoverable by tuning ITMY A2L.
The most intersting changes are at high frequency (>500 Hz, see spectra and ratio to nominal values). Moving CAM_YAW2_OFFSET has a small (3%) but noticeable effect on the sensitivity at high frequency. Not sure what's causing this: I don't think the change in power is large enough to account for a shot noise improvement, nor is the optical gain change. I think this is worth move investigation.
Analysis code attached.