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The primitive Wigner-Seitz cell, and corresponding first Brillouin zone (FBZ), is typically used for calculations of lattice vibrational properties as it contains the smallest number of degrees of freedom and thus has cheapest computational cost. However, in complex materials, the FBZ can take on irregular shapes where lattice symmetries are not apparent. Thus conventional cells (with more atoms and regular shape) are often used to describe materials, though dynamical calculations are more expensive. Here we discuss mapping of conventional cell dynamics to primitive cell dynamics based on translational symmetries and phases. This leads to phase interference conditions that act like conserved quantum numbers that enable a conventional cell description of vibrations and transport at nearly the same computational cost as those done in the primitive cell. We demonstrate this dynamics using first principles calculations to simulate phonons in two technologically-relevant magnetic systems: the cleavable antiferromagnet CrCl₃ and the quantum spin liquid candidate a-RuCl₃. Additionally, stacking fault limited, low temperature phonon transport in a-RuCl₃ is examined with regards to measured data, thus providing physical insights into thermal Hall behaviors of Kitaev spin-liquid materials.