I recently drove my 4WD to Cameron Corner, going in via the Sturt National Park, and then heading west and up to Innamincka. There is no way that I'd take an ST on those tracks. In many places the tracks are in fair condition, but in others it's heavily corrugated, sandy or very rough. We encountered a wrecked motorcycle trailer left on the side of the road 20 km west of Cameron Corner, and caught up with the owner/rider at Cameron Corner. The rough track broke the suspension on their heavy duty motorcycle trailer, and he was trying to arrange to have the trailer picked up and repaired.
I strongly recommend that you leave the ST home and explore those regions with either a 4WD or an off-road bike, which are both designed for those conditions.