I can't say it will work for you, but I went up there a month ago without any permit, camped in my car overnight and then went down the next morning. They had day permits for that day but I was looking for overnight permits for the next day. Day permits for that day are opened up at 8am, overnight permits for the next day are at 11am ( the lottery is just to see who gets to be in front of the line when you go inside to see if they have any permits available - and only one of you needs to be in line) I didn't have any luck this way but I had put the receation.gov page on my phone and was always checking it, so within an hour of leaving the visitors center I noticed that some had become available and I could pick them up at the visitors center ( there were 4 - and the weather might have scarred them off at the time). I scored !! Its not a guaranteed way, but try to keep all your options open.
