I would also highly recommend taking for example an SAT II type test in your second language…if it is a language in which such tests are available. My perception based on things I’ve read is that colleges care even more about standardized testing for homeschoolers than they do for traditionally schooled individuals.
I would also double check that info about homeschoolers not needing a counselor recommendation. My daughter’s significant other was homeschooled and he did need a parent to write a counselor letter. (I will also state, however, that he applied to an entirely different list of colleges than the ones you list above.)
In terms of the UC system, I found this fairly recent thread on College Confidential which seems relevant!
http://talk.qa.collegeconfidential.com/home-schooling-college/2128889-any-luck-getting-into-ucs-as-a-homeschooler.html
I would also use this resource, as I think talking to a network of people who have already been through this process would be immensely valuable.
https://hscollegebound.com/networking.htm
Best wishes for a very successful college search!