Even though you're allowed to submit your section of the application starting Sept 1, usually its the LOR's which keep your app from being complete. The best thing to do is to ask around to the current 4th years to find out
1. who's a good letter to get (like known names, etc)
2. did they have to badger the LOR writer until the very last minute
A lot of variation occurs across the board. Some people will have the letter in a couple of weeks and others you'll be waiting months.