Bears, I'm really sorry to hear about all this. You certainly didn't deserve it and the world would be a far better place if more people stepped up and tried to help others, as you did.
A couple of points on this. I think Flamingliberal is right on the domestic violence part of this. I am certainly no expert on California law, but I think that you were not involved in a domestic violence situation. The other two were, but you were the victim of a independent battery. I do hope she is right about there being another way out of the lease, though.
Similarly, there is no sexual battery that occurred here because the state has to prove that the suspect's intent was lascivious (i.e. there was some sexual gratification from it). That's not the case here. It is a battery, though, and generally they carry the same punishment anyway.
Before I say this next part, I want to say that I am no defender of the LAPD. They are an embarrassment to modern American law enforcement. This is made worse by the fact that most of our television and movie productions make them out to be the best cops in the US. They aren't and, in fact, their culture is probably the least helpful and service oriented of the major police agencies. There are, of course, exceptions and what kind of service you get from an officer is entirely dependent on which particular officer happens to show up. I'm sure that LA has some very good cops. The culture of the LAPD lowers your actual statistical chances of finding one unfortunately. Whatever your or my view of them is, however, they are the police agency that you have to deal withy on this.
Certainly, you can contact the DA, but I think the more productive step at this point would be to contact a police supervisor. I know several people recommended filing a formal complaint against the officers involved, but I'd hold off on that for now. That's because internal affairs complaints tend to slow down the entire legal process and set everyone in their current positions because they now have to defend their actions from an outside entity.
Better that you work within the supervisory system to explain your concerns that the officers didn't place the appropriate charges and didn't fully document the incident. I picked those words on purpose. Stay calm and speak politely. Not because something's wrong with you, but because the supervisor is far more likely to listen to you and do something about the situation if they perceive you as a decent person who has been wronged instead of an irate person who may have been a contributor to the fight. However angry that last sentence may make you, remember that these people have never met you before and are forming their opinion of you when you speak with them. Ask the supervisor how you can have the suspect arrested or charged. Don't tell him/her that they have to charge the suspect. It's important that your conversation not be confrontational. Not because the police officers handled the situation well (they didn't), but because you have to resolve the situation as it already stands.
Start with a sergeant and give him a little time to actually resolve the matter before going further. He/she isn't going to just say you're right when you speak to him the first time, they will speak to the officers involved first. You and me and everybody else would want our supervisor to do this someone complained about something we did, too.
If you're not satisfied, ask for the name of the lieutenant who supervises them. repeat and remember that a captain ultimately supervises all of them. If you get no satsifaction through the captains rank, then just file a complaint and know that the LAPD is even more hopeless than I already think it is.
Again, I'm very sorry you've had to go through this. I'm proud of you, though, for staying true to your principles and trying to make a better world by helping others. I wish you the very best in recovering and dealing with the justice system.