I suspect the difference in gravity between when the Moon is overhead (or at the nadir) and when it is sideways would be much less than the effect of the consta

I suspect the difference in gravity between when the Moon is overhead (or at the nadir) and when it is sideways would be much less than the effect of the constant small tremors that would be felt if the object was set on solid ground. Maybe a kind of low-pass system would allow it to react to slower change and ignore the higher amplitude, higher frequency of the tremors， though.