Over the past few years, the "Late Summer" deals have typically ended right around the end of September. So, as long as you aim for end of Sept to start the trip, you should fall under them IF (that's a big if) they follow the same pattern.
For example, this year I went with the FD promo for my 9/27-10/6 dates. Technically the promo ends on 9/28, but since it's a package, you can come in before the end of the deal and keep it for the whole trip.