Both ideas top my list of suspects... That is, interference generated by appliances and electronic equipment in your home, and aircraft induced multipath.
http://flightaware.com/live/airport/KLAX shows arriving commercial aircraft flying over the Culver City area which then turn 180° to fly the final approach into LAX. There is also a corridor for general aviation over the Culver City area.
To fight the interference caused by signal reflecting off aircraft, try moving the antenna to a location that has a clear view of Mt. Wilson but is 'shaded' by an eve or carport roof. The goal is to block the signal reflected off the aircraft, while still receiving a strong direct signal from the transmitter. Tilting the nose of the antenna may also help, though the clamp assembly on that antenna may not give more than a few degrees of range.
Your TVFR clearly shows you have no need for any sort of amplifier. With the signals as strong as indicated and the gain provided by the HD7694P, you should have no problem supplying as many as eight tuners using only a passive splitter.