We Republicans believe in competition and we believe that reasonably affordable housing in Los Angeles County for someone like yourself (or myself) could be achieved by tweaking and rebalancing how communities compete to attract you and your family. It is possible, and necessary, for policymakers to get creative in this space because it is a severe problem and folks are leaving California.
As you know housing trends in California are greatly influenced by the famous "Third Rail" of California politics, 1978's Proposition 13, which helped a lot of folks, but ultimately grants enormous advantages to families already established in California. These are the Big Winners of the game created by Prop 13. They speak of "cashing out their golden California ticket" when they sell.
One proposal to directly address your concern is the following: modify state law so that a community can opt-in (by a formal plebiscite in that community) to a gradual revocation of Prop 13 with each new transfer of property, and in exchange, local schools immediately get preferential funding.
For the sake of argument, let's say this change was ushered in by a new ballot proposition named "Prop 23".
This proposal is typically Republican in that it puts the action bottom-up into the hands of the citizens, market-style, instead of top-down Big Government-style, it doesn't coerce action, and it doesn't change the rules on folks who already planned their lives in order to win the golden Prop 13 game. But it allows energetic younger families to get better rewarded for what they are contributing to the state and to the community. Theoretically, as years pass, there would be "Prop 13 communities" in Los Angeles County that would miss out on the most energetic young families, and "Prop 23 communities" that would attract a higher concentration of these desirable families. Competition would intensify and it would speed up the process. Directly addressing your concern, our estimate is, as a side effect, that home sale prices would decrease in the "Prop 23 communities", making them more affordable (but of course, without a future Prop 13 advantage for these home buyers). Over time, this new system would change the character of real estate in California.