Look into working directly for a fire department as an Ambulance Operator (AO). According to Firecareers.com the following agencies in LA/OC are hiring AO's: Hermosa Beach and Downey. There's a couple others around too. More than likely my department (Glendale) will be hiring AO's again (the current new class is just starting backgrounds so more than likely after a few months once they've made it through those and gotten into our AO Academy we'll be testing the next class). Shameless plug for Glendale: Unlike some other FD AO's, all our ambulances are BLS ambulances staffed by AO's. The medics are on the engines and will hop on over to our rig and we'll transport ALS that way, some other departments that have a mix of Paramedic RA's and BLS AO ambulances will only dispatch/let their AO's transport BLS calls so you won't necessarily get much in the way of ALS assist experience, but despite that, I'd still take any of those over a private company in LA/OC nowadays, the experience of living in house will be invaluable when it comes time to interview for the coveted firefighter job in LA/OC.
In addition to that, I would advise not only getting your medic license ASAP, but completing a State Fire Marshal approved Basic Fire Academy. Most smaller and many of the mid sized departments won't even accept an application if you don't have your FF1 cert from one of the academy's. For example, Riverside FD is accepting applications in October, and will require an academy (and they're not a small, two engine department either). Plus, with your FF1 you can do volunteer/auxiliary/reserve firefighter (yes there are at least two volunteer fire departments in Los Angeles County, La Habra Heights and Sierra Madre), I personally also want to look into volunteering with Sierra Madre Search and Rescue....Those certs and experiences will immediately separate you (and hopefully me lol) from every other EMT who thinks their Care/Gerber/GCTI/TransAid/etc transport time and year old CPAT/fire academy they've done nothing with in the meantime