Having driven CVR within the last several days, you're making the washout seem a lot worse than it actually is. One thing to keep in mind is that the road is wider than it looks--don't be afraid to get friendly with the soft branches along the side of the road. The other thing is to avoid riding in the ruts (though on CVR, they're not bad), the washout is kind of like a deep rut, if you stay to one side of it, you'll be fine. Finally, just remember to go slow in general and really slow in the few rough sections.
There's no reason why you couldn't do CVR in many non-4wd cars, though a Honda Civic's clearance might be pushing it. If you're really uptight about your car, rent one for the day. But, if you own an Outback, you owe it to the car to drive it all the way up to the bridge with the red handwritten "Not safe..." sign, 1.1. miles up from the AT crossing (which, is very easy to drive by).
(If you want to practice, go to your local ski area and drive up and down their maintenance roads.)