Hitching West
Walk West towards the intersection of Creedon Street and Barrier Hwy. Like anywhere in this area, there is plenty of space to pull over.
Especially the "Grey Nomads" (retired people with caravans) will leave quite early in the morning towards either Adelaide, Peterborough or Port Augusta, so make sure you have an early morning start no later than 8am.
A good hint would also be to have a walk around the caravan parks in the morning and have a chat with some people who are about to leave.