Agree... my question, though poorly worded, is less about proof of spacetime gradients (they do in the ways you describe).
It's more about understanding what the measurable effects of a gravitational well on earth has on the LIGO experimental setup (or a similar one with infinite precision), in the absence of gravitational waves.
Well, something like LIGO can only measure gravitational waves, because it looks for changes in the geometry of spacetime. If you were to move the LIGO in and out of Earth's gravitational well, I guess then it would record a shift.
It's more about understanding what the measurable effects of a gravitational well on earth has on the LIGO experimental setup (or a similar one with infinite precision), in the absence of gravitational waves.