Try Ameriflight. Still a paycut for you, but they do have some SoCal bases. They don't have and jets, but if you want into part 135 having some 135.299 and 135.293 rides will help your resume. Plus, I know you said you're not too concerned about getting TPIC to go to a major, but lots of operators will still want to see it. Ameriflight has mostly turboprops but it still checks the box.