Actually, the weak nuclear force interacts (roughly) equally with protons and neutrons, so that won't work.
I know. I was thinking more about the effect on cross section from the density and size of nuclei, and thinking back to my lectures on how materials for the various neutrino detectors were chosen - the only issue being how long ago those lectures were

The collisions are shockingly low energy, actually. The earth's orbital speed is only about 1/1000 the speed of light, which is similar to what we believe is a typical DM speed in the galaxy.
Ah, yes, that'd do it.
I'd recalled some reading a while back that suggested that what we'd likely see in detectors was the DM equivalent of a high-velocity star, that has come out of an interaction with a bunch more energy than the run-of-the-mill particle. The piece included some cogent thoughts on the velocity distribution, and justification for thinking that such particles would be common enough to detect, and more likely to be seen due to the higher energy.