Earlier quoted context omitted.
Having recently done some moderately frustrating builds for the first time since my age was in single digits, I discovered that a small amount of pre-sorting radically improved this situation. And it doesn't seem to matter what parameter you index on: colour, size, type - anything to reduce the search space seems to work. Nor does the sort need to be complete. Just reducing the size of the unsorted pile also helps.
Then kids play once and wreck your presort.
Teach them how!