The current Carpet driver is not compatible with the periodic boundary conditions (as provided by the Periodic thorn or otherwise).
Erik's comment on the User's list was: "It is straightforward to implement periodicity in the grid structure -- one needs to take the current grid structure, shift it in the 26 directions, and take the logical union of all 27 grid structures. This will then be automatically clipped. The most complex part is calculating by how much to shift."
Please implement support for periodic BCs in Carpet. This will directly enable production science runs.