Here's a few humble suggestions:
1. Create your own opportunities, don't wait for the phone to ring.
2. You know the scene you want to get into (as described above) - Find this scene in LA. Ideally, that could be a collection of interfaces such as a website, a magazine, a physical area of town or a selection of venues, bars, clubs. Then, go hang out!
3. Put on a happy face and smile alot - You may have no idea how important that is. Simple hey?
4. Remember this - Many people may want the same thing you do, but only a select few know how to get it (and they usually do) More often than not, it's the NON musical aspects of a musician persona that gets the gig - and more importantly... keeps the gig.
5. Be genuine.
"Look 'em in the eye and give 'em a warm, firm handshake while smiling like you missed 'em for 10 years." - A LOST ARTFORM these days.