The Landau theory used by Choi and Mele (CM) to treat their rotor model on a triangular lattice for the orientational ordering of polyacetylene chains in alkali-metal-doped polyacetylene is studied. A reanalysis of the higher-order terms in the Landau expansion indicates that cosine ordering can support a nonzero cubic term in the Landau expansion whereas the sine-ordered phase has no such term. To construct a phase diagram requires a numerical solution of the self-consistent equations of mean-field theory. Although this analysis does not convincingly treat the incommensurate phases found by CM, it does identify an unusually rich variety of thermodynamically stable phases and leads to significant modifications of the previous phase diagram. However, we do confirm the principle result of CM, that alkali-metal doping tends to destabilize the herringbone phase that exists in the undoped system. We also identify a number of interesting multicritical points. At one of these, the quadratic terms in the Landau expansion are totally independent of wave vector. This situation is similar to that for the kagomé antiferromagnet.