Continuous state DEC-MDPs are critical for agent teams in domains involving resources such as time, but scaling them up is a significant challenge. To meet this challenge, we first introduce a novel continuous-time DEC-MDP model that exploits transition independence in domains with temporal constraints. Moreimportantly, we present a new locally optimal algorithm called SPAC. Compared to the best previous algorithm, SPAC finds solutions of comparable quality substantially faster; SPAC also scales to larger teams of agents.