3/2 Engineering Occidental/Columbia or Caltech OR Transferring to USC after 2 years

Obviously, financial aid can be uncertain if you transfer.

You could always apply to USC and other schools in your second year for regular junior transfer; if you get admitted with enough financial aid, then you can decide whether to choose to transfer then, or stay for 3+2. In this case, transferring then would likely be preferable, since you would not have to risk the uncertainty of Columbia 3+2 admission and financial aid.