Unfortunately, I'm not sure there's any trick to it other than saving aggressively as possible and keeping the money in a fairly liquid account. You could also roll the dice and put your savings directly into a taxable brokerage account if you don't mind the fairly high short-term risk. Of course, if you're struggling to save that much in the first place, the risk may be worth taking.
I have a number of friends in HCOL cities. Most of them plan to rent forever and many of them could afford to buy if they wanted to. To them the housing prices just don't make sense and the rent vs. buy calculation is skewed highly towards renting. Renting isn't a bad thing in the right market, and there's no reason to push towards home ownership just because "that's what you're supposed to do when you grow up".
Further, you mention that homes are appreciating faster than you can save. I would guess that over the course of many years, this appreciation won't continue at the same rate. But no, you're not missing anything, real estate is just crazy right now in pretty much every city on the West Coast. Focus on your savings and debt and don't feel bad about renting, it's the smart decision right now anyway.
And yes, it's totally fine to put down less than 20%. Piggyback loans are a great idea and even PMI is not the end of the world when you calculate it out and plan for it. Just don't get caught thinking that the standard 'American Dream' of buying an 80/20 house in a HCOL city with a reasonable middle class job is the norm anymore.