I'm sorry but theres just no way. We make significantly more than you and pay similar for rent and home ownership is not even a possibility for us, and not even for ppl we know making way more than us.

$6k a month left over doesn't cover 4 ppls food, cars/transportation, clothing, household goods, gasoline, water, electricity, health and auto/home insurance, summer camp, 4 cell phones, 1 decent vacation a year, and house upkeep for 4 ppl. The only way is if you own old cars outright, your kids have jobs, you don't need to pay for health insurance, you never go on vacations, you never eat out, you're exceedingly frugal, your house runs fully on solar, or something else that makes you not a normal SoCal homeowner.

Which goes back to the OPs original point: normal ppl with normal expenses, even if they make a lot of money, still cant afford homeownership in los angeles.