Just another thought: it has just occurred to me how close Lake Torrens is to Andamooka, ~20 mins drive (13km). Would be a good disposal site if one was to drive there in the middle of the night and on the way back get rid of a car at Blue Dam, which is just a few hundred metres detour from Lake Torrens rd.
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Pic of the area zooming out for reference as to the size of Lake Torrens
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JMO
ETA: the 26 mins indicated in the map is including the detour. From Andamooka to Lake Torrens and back without detour is ~20mins each way.