Throwing a number at you, based on NASCAR's 5/6 mpg, I doubt you'd need more that five- unless you drive back.
Stan Back has a Moon tank no more than 3 1/2 gallons. He's over 3000 lb and a crappy Cd (St Rdstr) goes 210, but tows back. Of course, he's cheap and makes the minimun number of runs to accomplish his goals. Don't think he ever refuels. Well, maybe once every two years or so.
Surprised you haven't had many experienced racers respond. 4th of July vacancies on the site, perhaps!