Have driven the Warrego once or twice but have never been through Tyrconnel. Google earth tells me it's off the beaten track. Just get fuel in Roma or Morven. If you're coming from brisneyland, Roma is about 5 hours. Lunch at KFC
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I don't recommend Morven - LRE after dark unless you are in a truck with plenty of steel up front.
BN - LRE is a big day. Have done it in 12hours illegally years ago. The cops are a tad meaner these days.
Enjoy the trip. Stay a bit longer in Kuntaburra. Might save you a trip deeper into wawa land