I'm pretty sure the primative camps can't be reserved more than 24 hours in advance of getting there and you can reserve them on the phone with the rangers. They may be difficult to get.
Another option is to check Big Bend Ranch State Park, which sits on the west side of the National Park. It's not heavily used and also has a bunch of primative campsites in the backcountry that you can drive to.
Sorry you didn't get a response sooner
