You never really know when a push is going to happen.
Mid Sept through Mid Oct is the best bet IMHO -personally, if your only going once, hit early Oct or very late Sept. to increase the odds a bit in your favor.
In the DSR the fish are just entering the river and move on through and then spread.
On a Saturday in Sept or Oct its combat fishing most places and the DSR is actually a decent place to be- if there is a push.
There is no memory like water splashing upstream towards you from tails of hundreds of fresh Kings running right at ya for an hour or two non stop---
Only happens down in the DSR before they spread out---
Hope it happens to you.
August or very early Sept reports can make ya nuts at home reading them but are generally from guys who fish often and know the river VERY well or are a bit overhyped compared to the main part of the run.
Occasionally it happens then but it just the start of a whole season -might want to wait it out an extra week or two and increase your odds.