You can do some rudimentary localization by latitude, however, by comparing satellites in different inclinations. You also get data by altitude, of course.
Something like this: https://en.wikipedia.org/wiki/GOCE
Easier to look at the altitude loss and infer the acceleration indirectly. With access to the raw higher time-resolution altitude data, mapping should be possible.
SpaceX has in the past gone above and beyond to expose TLE data for scientists and astronomers[1], so it's possible that people inside SpaceX would be open to collaborating on such a project.
[0] https://www.pcb.com/sensors-for-test-measurement/acceleromet...
A bulge would not homogenously slow all satellites, each one would be slowed by a different amount depending on its particular path through the bulge. Those that pass through more of the bulge will be slowed to a greater extent than those passing briefly through. Satellites in different orbits tell you where the bulge is, satellites in the same orbit tell you how the bulge is moving.
There is a fair bit of statistical rigour described in the original article at : https://www.spaceweather.com/starlink/starlink_drag_explaine...