I think it might be faster to have only two drivers. You're killing your time by having three people have to pee, etc., at each gas station.
Given the fact that they averaged 65.64 MPH (7008 miles/106.75 hours), I think it would be pretty easy to knock at least a few hours off of that time. I drive pretty fast on the interstate, and I'm able to average anywhere between 72 and 75 from Miami to Chicago, and that's driving with a woman and two dogs that each have to pee at every stop.
I'd love to try to beat their time. I've got a buddy who just stopped by our house for a night on his way back home to St. Louis (he stopped in Maine and Key West on his way here) who I've always planned to try driving the entire Pan-Am highway with, but perhaps we can warm up by doing the 48 states trip in under 100 hours...