I think the initial tests would be computer models. Take models of how the earth's core and mantle work (or the Oort cloud) and intersect that with models of how dark matter is spread through the galaxy. Are there inputs where the models behave as predicted, and are the inputs in any way realistic?

Wait 30 million years to cross the galactic disk again? /s

Maybe we could find a statistical difference between systems that are passing through the disk now and those that aren't.