The week after Labor Day for sure! We use Magical Vacations Travel and they usually have great deals that week as well. http://www.magicalvacationstravel.com/
I just looked at the prices, and the B resort has rooms for under $100; less than you would pay for AS (unless you had a very good discount) and the Hilton only slightly over $100 - far less than a Disney Moderate…
When I looked (admittedly a couple of months back) it was about $300/night (including fees) for a 1 king 2 bunk bed room for a week in early June. I’m amazed that the prices have fallen that much since then.
For anyone who’s interested: I’ve booked now! We are staying at ASMu from the 29th August to the 6th September and AKL Kidani Village from the 6th to the 12th! Thanks for all the help