Aren't more massive particles smaller though (in terms of de Broglie wavelength, at least), so they'd have a smaller "shadow"? Or do different forces have different cross-sections with different relationships to mass, so a particle's "size" is different for different interactions (and could be proportional to mass for gravity)?
Actually this is currently blowing my mind: does the (usual intro QM) wavefunction only describe the probability amplitude for the position of a particle when using photon interaction to measure, and actually a particle's "position" would be different if we used e.g. interaction with a Z boson to define "position measurement"?
The momentum wavefunction (or more properly, the wavefunction in the momentum basis) completely determines the position wavefunction (wavefunction in the position basis). And we can probe the momentum wavefunction with any particle at all, by setting up identical (say) electrons and seeing the momentum they impart on a variety of test particles. That is to say, the probability distribution of momentum of a particle does not depend on what we use to probe it.
As the position wavefunction is now completely determined in a probe-agnostic matter, it would be hard to justify calling a probe that didn't yield the corresponding probability distribution a “position measurement”.