I think I would opt for the mid-week rather than wait until October. Not only is the weather a risk, you have very long nights, too.
Mid-week, if you simply plan on showing up on two consecutive days at 9 AM at the visitor center, is practically a sure thing.
You can get a jump on permits, too if you start calling one to two weeks before your trip. A few good people actually call in advance and release their unused slots.
