An obvious solution to insufficient parking is to charge for it, see e.g. the book "The High Cost of Free Parking". This would motivate people to use alternative transportation (if it existed) and to carpool, take Lyft/Uber etc. With the proceeds from parking, perhaps a shuttle could be subsidized that would go from a friendly parking lot (unlike the exclusive Los Altos Hills neighborhood that doesn't want other, lesser humans to park on their streets).
I've been avoiding going to Rancho San Antonio for years now because of repeated frustration of trying to park there, even on weekdays. As a Mountain View resident, I can't just walk or bike to the park, because it's too far.

Part of the solution is that we just need more parks.
NOT athletic playing fields.
NOT water-guzzling lawns.

PARKS with lots of big trees (i.e. Redwood Grove in Los Altos), shade, and trails suitable for all people: young, old, handicapped, babies with strollers.
Parks that connect to walkable neighborhoods.

So that we can just get out and walk instead of drivings miles away to posh Los Altos hills and look for parking in Rancho San Antonio.

@Bay area hiker: Charging for parking is NOT an obvious solution. All that means is that whomever is charging will be making money, often from tickets from people who do not get back to their cars in time. Finding some other remote parking lot (where would that even be?) sounds easier than it is. And so that people can line up forever for the few shuttles to go back an forth? In the end, like every other paid parking solution, all you do is make access to the park easier for well off attendees who don't care about the parking fee, while people with less resources are disproportionately forced to bus in, eventually giving up and leaving the park to the rich.

There is no easy fix. You either build more parking, or you open more parks. Since there are not a lot of available open-spaces magically appearing and opening soon, and environmental concerns are not going to allow more lots, status quo is pretty much your only alternative.

It seems that there is a lack of recreational hiking space in the Bay Area. Making more parking will only crowd up the parks. It is a good thing that people want to hike and discouraging visitors by not having parking or by charging will prevent people from hiking.

Is that the desire?

All over the Bay Area there is more housing and less and less space for recreation. Every community should be thinking of improving access to recreation of all sorts, not limiting to those who can only bike to reach them.

I've been hiking Rancho San Antonio for decades, and it has gotten more and more crowded. Adding more parking will only increase the congestion on the trails. Not a desired outcome. It's been hard enough hiking around the busloads of tourists who dawdle on the trails and make a lot of noise.

Charge for parking? Why not. Reserve a day at the park ahead of time? Why not. But don't add more parking, hence more people.

If we simply open the trails to cars there will be no need to park. I get the feeling that many here would support an entirely drive-thru Rancho rather than come up with any alternative that takes them out of their car anywhere that's short of their final destination.

Why stop with only letting cars on the trails, just let them go anywhere and/or pave over the whole preserve.

Pinnacles uses a shuttle system, Yosemite has two bus systems. De Anza has plenty of parking available on the weekends and is not far away. County Parks is familiar with reservation systems for both camping and boating. None of these ideas are within Mid-Pen, but the study should be able to bring them forth. BTW this morning at 8:30 I counted more than fifty empty parking spaces.