On the washboard sections you need to adjust speed rather carefully to avoid vibrations. You can be hammered at 5mph, but smooth at 27.3. What feels best for you is probably also best for the vehicle and the tires. And keep an eye out on the road about 100 feet ahead. Of course when you come to those sand and rock moguls towards the end of the trail you need to slow down, but still remember that if you loose forward inertia in a sand trap or mud you are SOL, which is why you put a long tow strap in the trunk. Old fashioned, big-link snow chains might not be a bad idea in those areas, come to think of it.
And, no worn down tires please.
Or use a dirt bike. You can rinse off the 2 inches of dirt and mud at any of the many deluxe public hot tubs at the site, or just climb down a few thousand feet to the river for a rinse.