Driven both by humiliation and escapism, I have devoted some more
time to thinking about this problem and I believe I now understand
something I never appreciated before: The apparent gravitational
field strength undergoes a relatively large (first order in the ratio
of the radius of the Earth to that if its orbit) SEMI-diurnal
variation due to the rotation of the Earth, and a MUCH smaller
(second order) diurnal variation.
To first order, I find that g is the same at noon and midnight and
both values are smaller than that at dawn and dusk by about
delta g = 2 G M_sun R_earth/(R_orbit)^3 ~ half a micrometer/s^2
I am going to try to write up a brief analysis, which serves, I
think, as a very nice illustration of the use of the equivalence
principle) and will share later, if I haven't by then moved to Fiji.