I just got back Monday morning, and stayed on Kauai just off one of the roads you described.

I would not go far in a regular car on the unpaved roads in the Waimea/Kokee area. They seem to not be well maintained, and frequent rain (several times daily) keep them soft & gooey. In dry weather, good clearance should get you through, but I think the rainy season is starting--we had drizzle off & on most of our time up there.

Waimea Canyon is astounding! I'd advise 1) watching Jurassic Park before you go (it was filmed there), and 2) consider a scorpio boat ride around that end of the island (which I didn't do, but can only imagine).

Have a great trip!

JP