So i contacted the park and told them I was coming on Thursday, they told me to go to the right when I enter the park and go to camp C. It sounded like there would be room for others there too, but I did not know if anyone else had contacted them yet.
I'm still undecided on which way I will take to get there. Going straight up 29 to 64 to 81 is definitely shorter but mostly mountains. 85 and up through DC is much flatter, but it goes through DC.