We have the same issue, Westside of LA, lots of cash (although not as much as yours), a timeline that's at least 18 months out to buy, but no certainty we'll buy in LA or even at all at that point. We have the kids already, though. I also believe Westside housing prices are insane and they must come down at some point.
I'm considering the following plan, though: $60k is enough of a downpayment to use if we move. Prices in West LA are nuts and must come down. Therefore, if we stay, we'll rent until our savings and reasonable house prices line up. Therefore, we should invest anything above $60k and wait for the market to help us and house prices to fall. Essentially more risk, the downside is if prices fall and the market falls simultaneously and we miss our chance, but it's also possible that inflation-adjusted prices fall because inflation rises, and then keeping cash, we'd risk missing that opportunity anyway because our cash will lose value due to inflation. We haven't shown the inclination to take that kind of additional risk so far in life, but I'm floating this plan to see what people think. For you, that would probably involve investing the $100k you already have in excess of $60k (or pick you own lower COL area downpayment level.)
What do people think of this idea?