The typical rule is that they cancel the rest of your itinerary if you miss a segment. I don't think calling customer service will matter.

Flight delays/cancellations can grant you some options, but in practicality that doesn't help you much as your LAX-SAN segment isn't likely to cancel or become seriously delayed 7 hours in advance.

You are probably going to have to fly it. (I'm assuming you're talking about a legacy carrier and a nonrefundable round-trip coach ticket here.)

Lots of stuff you can do in LA for a few hours. You don't have to sit in an airport bar the whole time...