Availability at HH dramatically increases the later you get into August. Early that month is still high season, but by the end of the second week all the sunbelt families are gone (their schools having opened by then). Three years ago, we got a 1 bedroom (the most limited category at HH) at 7 months for a stay starting on 8/16.
The guest demographics also change - by the later part of August, almost all the southern accents are gone, replaced by people from the U.K. and U.S. northeast.