Using any kind of rating as an additional criterion when indicators are equal is incorrect, if only because it puts tournament participants in unequal conditions from the start.
I wonder, is rating used in this way in any sports? I can't recall any such examples. Except perhaps weighing in weightlifting, but there it's the opposite - the lighter one wins.
I suggest using a simple, quick, absolutely fair (i.e., giving all participants equal opportunities) and limiting the possibility of match-fixing method - a coin toss.
In football, for example, a draw is used in some situations when indicators are equal.