If the surveyor was instead using a relative gravimeter, the latitude correction would also be made for the difference in latitude between Sacramento and Emigrant Gap, which is 42.9 nautical miles or 79.5km.
Your opinion is contradicted by your own sources. It's not only relative gravimeters where the results are corrected by latitude. The source you provided,
30 years of absolute gravity measurements in South America, said that the absolute gravimeter corrects for "the effect of the rotation of the Earth", which means all of it.
The process is controlled by a computer that corrects the
luni-solar attraction, the effect of rotation of the Earth,
the ocean load and the barometric pressure, providing a
final “g” value;
This paper below describes both absolute and relative gravimeters, and then goes on to say that "gravimeters do not give direct measurements of gravity". This means that neither kind of gravimeter is measuring gravity directly.
https://gogn.orkustofnun.is/unu-gtp-sc/UNU-GTP-SC-16-13.pdf3.4 Measurements of gravity
There are two kinds of gravity meters. An absolute gravimeter measures the actual value of g by
measuring the speed of a falling mass using a laser beam. Although this meter achieves precisions of
0.01to 0.001 mGal (milliGals, or 1/1000 Gal), they are expensive, heavy, and bulky. A second type of
gravity meter measures relative changes in g between two locations, see Figure 6.
....
3.6 Reduction of data
Gravimeters do not give direct measurements of gravity; rather, a meter reading is taken which is then
multiplied by an instrumental calibration factor to produce a value of observed gravity (known as
gobs). The correction process is known as gravity data reduction or reduction to the geoid. The
various corrections that can be applied are the following.
This statement that gravimeters are not detecting gravity directly shows that you are incorrect. As you describe it, an absolute gravimeter should be detecting gravity in full. Instead, it is really analyzing the vibration of the mirrors while the falling object is disconnected from the device for a more accurate comparison. It is using the same seismic gravity phenomena as the other referenced gravimeter devices, not something completely different.
It is absolute because the body in freefall is disconnected and not vibrating with the device, allowing a better measurement.