We went up around the same time you're looking to go, last year Sept. 30th - Oct 1st, and the weather was beautiful, pretty chilly, but no snow had fallen yet, so no need for ice axe and crampons. Fall colors were available for viewing which is always a very nice plus.
We went again exactly a month later Oct 28/29 last year, and we brought & needed ice axe and crampons (above trail camp).
So you see that a month can change alot... but your last weekend in Sept. hike should work well for you, not hot, less crowded, and there shouldn't be any snow to contend with.
Good Luck !!