I am a total layperson in this area but I think the GPS correction/frame dragging also incorporates relative motion where this (i think) is purely about gravita

I am a total layperson in this area but I think the GPS correction/frame dragging also incorporates relative motion where this (i think) is purely about gravitational field strength. To your point, maybe, I wonder if they had to factor in the relative velocity difference of the top and bottom of the cloud due to the rotation of the earth at their latitude (or just do the experiment at the south pole). At the equator, assuming a cloud of 1mm diameter, it would be 2π mm/day, which according to a sloppy google search is 2.425675e-16c.