I managed to reproduce the doctest failure by updating my local conda install to match the environment that Travis uses. I'll continue debugging tomorrow (unless someone else gets to it first!) ;)

The doctest was failing due to the fact that the source cube is now being cached (a new cube is created) in AreaWeightedRegridder. This means that when RectilinearRegridder._create_cube is called, copy_coords, didn't correctly copy the latitude and longitude coordinates (using is checks whether both variables refer to the same object, which is no longer true), which resulted in VOLCANIC_ASH_AIR_CONCENTRATION / (g/m3) (-- : 73; -- : 96) rather than VOLCANIC_ASH_AIR_CONCENTRATION / (g/m3) (latitude: 73; longitude: 96) (thanks to @stephenworsley for finding the root cause!).

__prepare is now called when the AreaWeightedRegridder is instantiated. This allows the use of src_grid_cube directly, without caching it, which enables the change I made that was detailed here to be removed. It's possible that target_grid_cube also doesn't need to be cached, since it is only now used in __prepare (which is only called once, when AreaWeightedRegridder is instantiated). However, I'm not sure if there would be any significant performance issues related to the fact that the cached target_grid_cube has no data associated with it.

Looks good. :)
Now, most of the checks on the src and target cube are done at the instantiation of the regridder. We then check that the src cube x&y dims match those that the checks were done on. At a later date we might be able to revisit the restrictions and reduce them a little. However this is not easy to determine until the weights refactor is in.