San Francisco to Grand Canyon Road Trip?

Head West to the ocean and make a left.

This will get you out of SF before the commute traffic.

Head South along Hwy 1. That will take you down to Monterey Bay. Going further down Hwy 1 will take you into Big Sur. While that is a beautiful drive, it takes a dozen hours or so to get down to another hwy to head to the Grand Canyon. So Santa Cruz or Monterey might be good for that first half day. A side trip to Felton and you can take a walk through the Redwoods in Henry Cowell State Park.

Then cut back east to go on down Hwy 101 for scenery or Hwy 5 for speed. There are vineyards along Hwy 146. You may want to make your way down to Antelope Valley and the California Poppy reserve. If they are in bloom there can be acres of rolling hills of yellow California Poppies. This is by Lancaster which takes you down through the Mojave dessert towards Las Vegas without going all the way into the Los Angels basin.

If Highway 1 is open, take it as far as San Luis Obispo. On the way, you can visit the Monterey Bay Aquarium and Hearst Castle. Then, get on Highway 58 east to Barstow. There, you can get on either I-15 north to Las Vegas or I-40 east to Williams, Arizona. You'll need to get to

Williams anyway to reach the Canyon.

That mainly depends on how much driving you want to do! To me it sounds positively leisurely. I did a trip to the same area a couple of years ago and we went with plans like yours (around 1800 miles originally) but ended up doing so so much more (around 4000 miles in the end) and we only had 10-12 days IIRC. We were a little tired when we headed home but, wow, what a trip! As I say, I really don't think you're being too optimistic at all. Also try hiring from good reputed company as they can give you a good deal along with good car and best of discounts.

If you're going inland from San Fransisco to the Grand Canyon, you can stop off at Yosemite National Park. If you're driving along the Atlantic Coast and then turning inland to get to the Grand Canyon, why not stop over somewhere in the vineyard areas?