How soon to submit applications

Don't concern yourself with what goes on behind the scenes. You can't control that so just focus on your applications. Like was said before - those schools don't have rolling admissions. What would it matter if you submitted your application and they read it that day vs. 3 weeks later? Even if they read it that same day, they wouldn't decide on whether or not you're admitted until committee review when they're all sitting around the table. And then you aren't notified until the decisions date so...again... don't worry about it.

word to the wise - when you think you're absolutely done with each application. print out all of your essays, transcripts, resume... etc... put it in a folder... and don't look at it for a couple of days. Then go back with fresh eyes and go through everything to make sure that it's perfect.