RE: Prop keeps falling off
Actually something that is being overlooked:
If your prop nut is "bottoming out", then it may not be exerting enough force to hold the prop in place, and as a result will work loose during start up.
Make sure that with the prop assembly in place the nut has plenty of available threads to go into when tightening down.
With a thin prop, on some engines, a shim or washer may be required to buy you the space to lock the prop nut down tightly.