Thanks to everyone who chimed in about the timing of the next round! After comparing it with the mods' availabilities, here is the schedule:

Nominations open: Monday, July 28 (will remain open through signups)
Signups open: Monday, August 4
Signups close: Monday, August 11 @ 11:59pm Eastern Daylight time
Assignments out by: Wednesday, August 13
Assignments due: Saturday, August 23 @ 11:59pm Eastern Daylight time
Collection opens: Saturday, August 30 @ 1:00pm Eastern Daylight time
Authors revealed: Monday, September 1 @ 1:00pm Eastern Daylight time