I have booked trips after Thanksgiving in October in the past without much trouble. I checked the online reservation system & you can book backcountry paddling & hiking with last date of Oct 26. So after that you would have to call in & I guess weather & conditions dependent you could get a backcountry permit. But anyhow, you would have to call in to book a Ranger cabin. All the ones that you can book online up to Oct 26, are easy to get to & would have already been booked up long time ago.
FYI, I was just up at the Brent Ranger Cabin for 4 days/fall viewing & it was a nice experience, although it also shakes my faith in humanity. There were several burn marks in the wood flooring (I presume carelessness with the wood fireplace, but I don't know how you would even do that as there is stone flooring for several feet in front of the fireplace...), burn marks on bedside table tops & mattresses (presume smoking in bed...). In a way I'm surprised the cabin has not been burned down yet, please visit & enjoy these treasures before some idiot burns them down.