I wonder how this compares to the sphericity of a neutron star.
A neutron star has a diameter of about 20km and surface irregularities are currently estimated at under 1 mm. (See https://www.livescience.com/millimeter-tall-neutron-star-mou... for verfication.) Scale that up to the Earth's diameter and irregularities are on the scale of 64 cm.
See [1] for more detailed discussion of how the Gravity B team pushed on with analysis in the face of systematic errors much larger than the effect they were trying to measure, to come out in the end with a believable measurement of the incredibly subtle effect of gravitational frame dragging.
[1] https://ddd.uab.cat/pub/tesis/2016/hdl_10803_400663/chev1de1...
One should always be open to the possibility of a failure, and do everything to meet it well-prepared!
For example, all the missions to the International Space Station are like that. They launch when the launch point passes through the plane of the ISS orbit.
Same group that "measured" a magnetic monopole and fractional electric charge, IIRC.