Your third approach seems to be correct since you aren't using animations.
Use QKeyEvent::isAutoRepeat () to find out if your handling an 'real' key press.
For fluid motion when a key is pressed i suggest you start a timer when a key is pressed and kill it when all keys have been released. You could use a QSet to keep track of pressed keys.

Qt Code: 
  1. //member
  2. QSet<int> pressedKeys;
  3.  
  4. void keyPressEvent(QKeyEvent* e)
  5. {
  6.     if(e->isAutoRepeat())
  7.         return;
  8.     if(pressedKeys.isEmpty())
  9.         startTimer(40);
  10.     pressedKeys.insert(e->key());
  11. }
  12.  
  13. void timerEvent(QTimerEvent* e)
  14. {
  15.     if(pressedKeys.contains(Qt::Key_Up))
  16.        ...;
  17.     if(pressedKeys.contains(Qt::Key_Left))
  18.        ...;
  19.     updateGL();
  20. }
  21.  
  22. void keyReleaseEvent(QKeyEvent* e)
  23. {
  24.     pressedKeys.remove(e->key());
  25.     if(pressedKeys.isEmpty())
  26.         startTimer(40);
  27. }
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This way you should be able to catch any combination of keys being pressed.