We characterize asymmetric growth of magnetic bubble domains in perpendicularly magnetized Co/Ni multilayers grown on seed layers by application of perpendicular and in-plane magnetic fields. Using a refined model of domain wall creep that incorporates contributions from the anisotropic elastic energy, ɛ, and a chirality-dependent prefactor, , we elucidate factors that govern the mobility of Dzyaloshinskii domain walls as a function of seed-layer composition. The interfacial Dzyaloshinskii-Moriya interaction (DMI) magnitude is found to decrease monotonically with , which is independently confirmed by Brillouin light scattering. Moreover, the persistence of significant asymmetry in velocity curves across the full composition range supports previous assertions that a chirality-dependent attempt frequency akin to chiral damping could play a critical role in the observed trends. This work helps resolve fundamental questions about the factors governing Dzyaloshinskii domain-wall creep and demonstrates varying Pt-Ir seed-layer composition as a method to tune DMI.