Hey Johnny,
Not really special permission, but I found out that the park service offers a "Twilight" tour of Cliff Palace. It's not very well publicized, and costs more than the standard tour. What's good, is that the max number of people is 20 and you spend around an hour and a half down in the ruins with a guide. It was a great learning experience and allowed for many shots of the ruins without people in the shots!
Joel