Around 9 A.M. on January 29,2013 there was a Boeing 747, Airbus A380, or Lockheed C-5 flying west over Santa Monica around the southern part of Santa Monica area then did a loop over the ocean then came back east over Santa Monica then it went out of sight. I looked at LAX flights on FlightAware and saw a Boeing 747 depart about 9:06 A.M. but it was a few minutes before that 747 departed from LAX. And no 747s, A380s, or C-5 were landing at LAX that I saw on here.
I can’t help you, but I would recommend posting something about this in the Notable Activity section, you might be able to get some more info there.
You also left off the possibility of the A340…