I havent paddled that route in 30 years..but the last of Sept and first of Oct has never been busy in the Canoe Lake area if you clear the immediate vicinity. There is the usual carnage at Canoe Lake but they all give up by Burnt Island. Then I have seen no one for the last two trips in the western part of the park. I have gone to Burntroot etc
I would suggest just go and not do the reservation dance.
No man should go through life without once experiencing healthy, even bored solitude in the wilderness, finding himself depending solely on himself and thereby learning his true and hidden strength. ~Jack Kerouac