For what it's worth, just directly measuring changes in gravitational acceleration is much easier and much more sensitive to changes in mass distribution. We'v

For what it's worth, just directly measuring changes in gravitational acceleration is much easier and much more sensitive to changes in mass distribution. We've been able to measure gravitational acceleration very precisely for over a century now. An 80-year-old LaCoste & Romberg gravimeter will do the job quite nicely, though it's slow to use and you need to know the elevation you're taking the measurement at very precisely. (Interestingly, the ones made before ~1950 are more precise than the ones made in the 60's to 90's. It's basically a very well made and well calibrated spring. When they switched to mass-producing them, the quality fell.) Now you have a second problem, though... Regardless of whether you've measured things through gravitation acceleration or time dilation, going from the measured effect back to an actual mass distribution is a non-unique inverse problem. There are an infinite number of equally correct solutions (and a larger infinite number of incorrect ones). You can make a pretty good guess at what the mass distribution by applying reasonable a-priori constraints, but there's no single unique way to get the mass distribution from the gravitational effect of the mass.