I'd make these changes:
Fly into Las Vegas (2 nights)
-- drive to Zion National Park spending 1 or 2 nights in Springfield UT or in the park
North to Bryce Canyon (3 nights)
-- don't need 3 nights here. 1 is enough.
Drive south to Grand Canyon (2 nights)
-- I'm assuming you want the South rim, not North rim. North would be a shorter drive, but all the developed facilities are on the South side. I'd do this after Utah rather than before.
Death Valley (1 night)
-- D.V. is extremely hot in September. Not sure when the entire park reopens for the fall/winter season, so check on the hotels. A ranger once told us that the only people she ever sees there in the summer are German tourists (or maybe Austrians?
)
Yosemite (3 nights)
-- from D.V. go out hwy 190 and then take US 395 north. You can stop at Manzanar National historic site for a couple of hours if you are interested. Then go north to Mono Lake and see the tufa before heading over Tioga pass (hwy 120) to Yosemite. Tioga is one of the most beautiful drives in the entire Sierra range and to my mind, much preferred over going around the southern way, though it's a bit more impressive going the other direction from how you're traveling.
San Francisco (4 nights)
-- lots to do here. Walk the GG bridge, Alcatraz tour, Fort Point, do the 39-mile drive, see a baseball game, visit the Marin Headlands and/or Muir Woods, Point Reyes light house, drive to wine country.
Coast between SF and LA (3 nights)
-- you've already heard about the Pfeiffer bridge outage. If it's not repaired by the time of your trip, use US 101 as an alternative. It's more scenic than I-5 and you can stop in Santa Barbara on the way to L.A. If you are able to drive on Hwy 1, then Monterey/Carmel and Hearst Castle are great stops. Also the elephant seals at Ano Nuevo.
Los Angeles (3 nights)
-- also lots to do here. You could focus on movie making and see the Chinese Theater, Hollywood sign, Warner Bros Studio Tour (Universal is more of a theme park so you may prefer that), drive Mulholland. Or maybe you'd prefer wandering around the OC coastal towns -- Laguna Beach, Huntington Beach, etc. Or Disneyland Resort.
It might be a little easier to reverse the stops after Death Valley and go to L.A. next, ending in S.F, but I assume you already have flights out of LAX.
The National Parks, especially Zion, Grand Canyon and Yosemite are going to be 100% full in September, so you need to make reservations for those areas ASAP. These three also operate shuttle buses and at least Yosemite and Zion prevent you from driving in some areas of the park. I don't know if GC also limits auto traffic, but I do remember they had buses last time we were there.