People transfer for that reason all the time. I wouldn't get too comfortable because the schools are similarly ranked though. The school you want to move to might not take that many transfers, or there might be more demand to move to that school than you think. Or the school may only take transfers with grades above a certain threshold, and not median or below students.
Are you waiting to start 1L at the SoCal school? If you haven't started yet, your best bet is to not start, and simply reapply with the intention of getting in the normal way.