I think you should go ahead and apply after getting in some more shadowing hours if possible, like double what you have. It could all be with one doc and you could get it done very quickly.
When adcomms look at your application, they'll see your year-by-year grades. It won't be immediately apparent that you had five quarters of excellence, rather it will look like one year's worth of high performance. I would proceed with the plan to take additional classes in upper-level science, including your classes and grades in update letters through the cycle, along with an update on the research and your current volunteering (which you'll need to continue through the application year). This will give you a lot to talk about at interviews, too, and if worse comes to worst, position you well to reapply if need be (with the newly earned grades listed on the Postbaccalaureate line, under Senior year grades). I do think you have a reasonable chance of an acceptance this cycle, though maybe not in California, and agree with "apply broadly" to a generous number of schools.
Do you have any Leadership to mention? And don't forget hobbies, sports, and artistic endeavors to make yourself look well-rounded and interesting. Overall, your listed Experiences look very solid though.
Use secondary essays to explain why your academic performance was subpar for so long. You are generally asked to discuss a Challenge you overcame, a Stress and how you handled it, or Explain blips in your academic road.