if you want a section, you generally (altho again, massive caveat based on ppl I know and our area) won't have an issue getting it
However, if you move out that late on, you'd basically need to be registering with an OB before you even arrive so they can get you in their practice / system and you'd need to be able to bring your notes / records with you.
LA and the surrounding area is MASSIVE so I'd be thinking about where you're likely to live and go from there in terms of hospitals and doctors. You can probably get good solid recommendations on local moms Facebook groups or similar for an OB (our local FB group is certainly peppered with requests for similar recommendations) and hospitals.
Worth noting that your nearest hospital might not be 'the best' and it's definitely worth looking for ones that have good reputations for birth and maternal and infant birth aftercare, as sadly, some places are terrible.
Also note that not all Drs have admitting privileges at each hospital - this basically means your Gp or OB is affiliated with a certain hospital (or maybe more than 1) and they are allowed to practice and see there patients there and nowhere else. If you get admitted to a place where your dr doesn't have this, they can't come and see you there
When you search for an OB you can ask or look for where they have admitting privileges, as this is where you'll deliver.
As a guide, on costs without insurance based on the original bills. My OB practice (so at the drs, not the hospital) charged $350 per visit to them, more for blood tests or additional scans. My straightforward section delivery was nearly $100k when they factored in surgeon, nurses, 3 nights stay, theatre costs, drugs, dressings etc etc. EVERYTHING is line itemed for expenses, down to the disposable knickers - its basically absolutely insane. However with insurance, this was all covered so we paid none of it
These insane costs are the reason good health insurance is a must!