Having driven this route on more than one occasion, I would have to agree, seven days is an absolute minimum. It is a most enjoyable drive off the Interstates, but can be slow going. Sleeping in a wagon can be OK if you have a mattress on which to get good rest. In May your sleeping bag will probably provide enough warmth.
But where are you going to park? Once off the Interstates, truck stops (the safest place to spend the night) are going to be few and far between. It may be worth your while to invest in a copy of the Trucker's Friend.
Lifey