Well, the Floyd was designed to be used with a locking nut, that's why it has fine tuners on the bridge.
If you want something that's much less hassle to set up, why not go the whole hog and ditch the Floyd altogether - try something like a Hipshot, Wilkinson or Gotoh tremolo, with the locking tuners and Graph Tech nut? They probably have a bit less dive-bombing range than a Floyd, but then you wouldn't have that problem of strings popping out of the nut.