G'day John.
Having lived in the tropics for 20 years (Darwin, Katherine, FNQ) and travelled a fair bit through The Centre, December is not the time I'd choose to travel for pleasure, as such. Whether the Simpson is open or not, I wouldn't consider it at that time of year. Of not for my sake, for the sake of the poor soul/s who have to come an rescue me in the event of a breakdown.
Options I'd consider, in the knowledge it'll probably be as hot as hades are:
Plenty Hwy to Boulia, continue to Winton (very picturesque), Longreach (Hall of Fame & Qantas Museum), Landsborough Hwy to Brisvegas.
South to Coober Pedy, check out The Breakaways just to north, across the Moon plain through Anna Ck Station to William Ck, down the Oodnadatta Track to Maree, thence Lyndhurst, up the Strzelecki Track, 120 km north of Montecollina Bore, turn right to Merty Merty station, then through to Cameron Corner, then NE to Noccundra or ESE through Sturt Nat Pk to Tibooburra then N to Nocundra, then Adventure Way through Thargomindah and Cunamualla to Brisvegas.
South to Port A Gutta, up through the hills to Quorn, Peterborough, Broken Hill, Wilcannia, up the Darling (either side), and so on.
At the risk of telling you how to suck eggs, take plenty of water and food, and beware of wet season/summer rains possibly making some roads impassable.