The use of patterned stress fields to direct phase separation in thin film alloys is investigated computationally with Monte Carlo simulations in which atomic interactions are represented by a Lennard-Jones potential.We show that careful design of annealing schedules based on consideration of the system phase diagram can lead to vastly enhanced patterning kinetics. In particular, by avoiding the low temperature formation of highly stable nuclei within the entire system, the kinetics of patterning are accelerated by rapid monomer diffusion, rather than classical Ostwald ripening in which small precipitates must dissolve to feed larger ones.