You apply now for 2021 spring. App period is now through Dec 15.
You can ferry a rig to Ketchikan from Prince Rupert or Bellingham and then over to the island.
Or you can fly up and rent a rig/boat/cabin from a few different outfits. Hollis Adventure Rentals, an outfit in Coffman cove, and one in Thorn bay.
You can rent Forest service cabins as well. Or just camp.