How would a cloud of ortho-positronium atoms behave near a magnetic dipole? The force on a macroscopic magnetic dipole with dipole moment $\mathbf{m}$ in an inhomogeneous magnetic field $\mathbf{B}(\mathbf{r})$ is given by 
$$\mathbf{F} =\nabla (\mathbf{m} \cdot \mathbf{B}(\mathbf{r})).$$
If there was a cloud of orth-positronium (triplet state, S=1, Ms=−1, 0, 1) near the equator of a large magnetic dipole field (i.e. a large $\nabla B_z$), would some be attracted, some repelled, and some unaffected? Would it separate into three clouds, moving towards, away-from and fixed with respect to the dipole field? 
Would the magnitude of the force be of order $\mu_B \nabla B_z$ with $\mu_B$ being the Bohr magneton?
It seems that I'm trying to treat the positronium molecules as little classical magnetic dipoles with quantized orientations, but I'm not sure if this is a good approximation.
 A: This idea is the basis of how pure magnetic traps for neutral atoms work. You have the idea essentially right, they're usually thought of as high-field seeking and low-field seeking states, determined by whether the z component (with z being the direction along the magnetic field) of the total angular momentum of the atom is parallel or anti-parallel with the magnetic field (so $m_J$ positive or negative). 
The size of the force is of that order of magnitude, but traps are more commonly characterised by a trap depth in temperature units. For antihydrogen traps with superconducting magnets (gradient of ~a few Tesla over a cm to tens of cm scale) that I'm familiar with this depth is around 0.5 Kelvin, so they can't trap atoms with more energy than this.
The standard treatment of point particles in quantum mechanics is to treat them as magnetic dipoles with zero extent, so that's fine too. I think stating that the orientation is quantized is subtly incorrect (angular momentum is quantized along one axis at a time, but there's an uncertainty relation which means it's always undetermined over the other two axes) but not enough to matter.
