Back when I worked in a music shop I used to insert the string through the peg's slot, then bend the end backwards (opposite of how the string will wind) and then wind the string over the end. This was thought to keep the string from slipping but I do not see anyone doing this anymore. Now everyone inserts the end into the hole in the middle of the slot and wind as normal. Thought?
If I install a string set (that was previously on another bass) and don't have at least 3 wraps for the post, to take the tension strain off the angle going into the slot, I use a 'one over, the rest under' locking wrap, similar to what you described. Haven't yet had a problem with it: round-cores, tapes or flats.