You have a sound plan for the UC’s. Go to a California CC, preferably an excellent one like Foothills, the transfer to Cal, UCLA, UCSD or UCI, etc… That path is prescribed, well documented and all of your credit will transfer with proper class selection. The other top private universities want you there for all 4 years and there are so few transfers (because so few people leave) that is is highly unlikely.
Spend the money you saved by going to a CC for grad school at one of those big name private universities.