Those earthquake and traffic nightmare stories are wildly overblown. The roving gangs of ex-convicts looking to relive their "prison love" days keep things interesting. But anyone who can run a four minute mile while dragging a suitcase and computer bag can usually outrun the gangs actively roaming the area around LAX. On the bright side, if you get caught, the LA traffic copters will probably catch it all on film, so you'll be famous just like Reginald Deney. So you've got that going for you.
Rather than a crashpad (which can be very expensive in the LA area), I highly recommend The Hacienda hotel. It tends to be the hotel of choice because its drivers will pick you up and drop you off at the FedEx ramp. Last time I stayed there it was $65 a night. But I always bring one of those backpack style hammocks and put on a wetsuit and combat boots once I get to the room to ensure I don't touch the bed or floors. The cleanliness isn't really a problem if you already have hep C and are immune to bed bug saliva. But you need a wallpaper scrapper to clean the shower fungus off your feet, and I kept getting it confiscated going through airport security which gets expensive. And those LAX airport security folks can get very aggressive (see paragraph one but replace "prison love" with "cavity search").
And welcome to LAX. You might get my locker because as of the last practice bid it looks like I'm getting excessed out.