Squatting in American cities these days is a pretty miserable state. States are starting to pass really repressive legislation to deal with squatters. It used to be that you change the locks, send yourself some mail and it becomes a civil eviction issue, so then when the cops show up, you leave and do it again somewhere else. Now it's becoming a criminal trespass issue no matter what you do if you don't have a rental contract in hand. California may not be there yet, but it's probably coming and you could definitely hurry it along by doing this out in the open. I would highly suggest keeping these things as much on the low as possible. Cops in LA do nothing 99% of the time, but if you do manage to get on their radar, they can be super aggressive over really dumb shit. I would say, try not to get their attention, don't poke the hive. Find ways to alert yourself if a landlord/management company person shows up and have an exit plan and don't get too comfortable setting up permanent living spaces. Be willing to get out at a moments notice.
The best way to end up with serious legal problems is to get caught cracking it. So I would say crack it one day, deal with the locks another day and then don't move in until you have sent mail to yourself at the address. If it's not too hard get something official in your name at that address... Electrical bill, internet, some kind of bill would go a long way in making this a civil and not a criminal issue, but I am guessing if you can't produce a rental agreement the police are likely to treat it as a criminal trespass, possibly B&E and if you produce a fraudulent rental agreement you'll end up with bigger problems.
Now those big towers that are all tagged up, you probably could easily squat. People have gotten caught tagging it and the owner didn't press charges, so you could probably live in there for a while and when you get kicked out, end up without any charges.
None of this is official legal advice (I am not a lawyer). You probably should look into squatting laws that are specific to LA, I am sure they exist, because politicians consider this a high priority issue in California.
