We have a feature in the app called 'Minimize Water Hammer' (Advanced device settings). This will keep the previous running zone valve open for 10 seconds while allowing the next zone valve to open. In a lot of cases this can cut down on the loud hammering noise you hear between zone runs. But it sounds like the real problem is just the water running in general.
Rain delay in the sense you want to use it won't work. If rain delay is set, and a schedule should run, rain delay will effectively skip that schedule.
The path to least resistance might just to create a couple of watering times, one for during the week and one for the weekend with different start times.
Hope you can find another use case for the API, love to hear people doing mashups.
Let us know if you have any other questions or feedback. Thanks!