Did you resolve this? I have EXACTLY the same problem. Flying at normal pace for the first 5 mins (according to Activity Monitor, using 350% of the CPU). Then all of a sudden, it drops to 35% of CPU (about 5 mins into the transfer).
If you really are in a jam and aren’t too concerned with a quality loss, you can always play it back in QT and then record your screen with iShowU or Screenium, or whatever. Then sync it with the audio from your original QT conversion (the one that gave you a white frame for the video).