I did a bit of climbing in Mootwingee about 10 years ago. Its nice quartzite but we had to remove heaps of large blocks to clean the faces up. I recall it was a bit scary at the time. heaps of potential i reckon. It might be worth contacting some of the stations that surround the NP. You might be able to access some of the more remote, less public spots from their tracks.
If you are going that far (Broken Hill) to climb then you might as well drive another 6 hours and head to "the moon". You won't regret the decision. You can take a shortcut from Yunta up to Cradock. It's dirt so it will probably take the same amount of time as going via Jamestown but its nice country.