I'm just curious....why stay in Ash Fork, AZ, for the Grand Canyon? Williams is probably a little more accessible and has quite a bit more choice of lodging in all budgets. It's right on the southern end of the highway that leads to the Grand Canyon South Rim. Oh, and you'd have to really hit a bad traffic situation for it to take you 12 hours to get there. It's probably closer to 9 hours, though I've seen some backups that were hours long.
If your flight is at 19:00, you'll want to be dropping off your car no later than 15:00. Meaning you should leave Santa Barbara in the morning. Better to have to kill time somewhere around LAX than to be late for your flight. Bear in mind that one of the worst traffic pockets in LA is around the intersection of the 101 and the 405, and you'll either need to avoid that or allow a bunch of time to get through it.
Donna