Perhaps give them another call? There seems to be one private room left here:
http://www.hostelbookers.com/propert...9/ngt/1/ppl/1/
We plan to leave Darwin at 4am, 1088 km to Devil's Marbles. Should be doable with early morning tea and a swim at beautiful Bitter Springs, Mataranka then lunch at Daly Waters Pub. Two drivers. You should be okay, just get some good sleep!