Symmetric higher-order Kuramoto coupling with transmission delay and the structural directedness of the interaction network are two independently studied routes to rich collective dynamics. We unify them in a reduced description that adds a single phenomenological directedness parameter ν ∈ [0, 1] to the delayed triadic Kuramoto–Sakaguchi order-parameter equation, through a forcing term motivated by, but not derived from, the desynchronizing action of leader nodes in non-normal networks. The analysis of the resulting delay differential equation, together with numerical validation including convergence and initial-condition checks, yields five results. First, the number of coarse dynamical regimes saturates rapidly with ν, unlike the multistability ladder driven by interaction order. Second, within the sampled parameter window, triadic coupling is associated with whether the population synchronizes, whereas ν is associated with how stationary that synchrony remains. Third, where subcritical bistability exists, the hysteresis loop narrows with ν under the finite-amplitude criterion used. Fourth, a directed asymmetry index D(t) grows modestly but monotonically with ν, independently of breathing amplitude. Fifth, the linear stability threshold of the incoherent state is exactly independent of ν, whereas a separately fitted finite-amplitude onset formula agrees with numerical continuation only over an intermediate range of ν; its failure outside that range is quantified. We discuss implications for neural, power-grid, and ecological networks, and state the limitations of the scalar reduction explicitly.