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, this paper first introduces a novel continuous time DEC-MDP model that exploits transition independence in domains with temporal constraints. More importantly, the paper presents a new locally optimal algorithm called SPAC. Compared to the best previous algorithm, SPAC finds solutions of equal quality substantially faster; SPAC also scales to larger teams of agents.