16 golfers enter. 4 rounds, played in similar manner to a bracket.
Round 1 - Top 8 of 16 scores move on, break all ties.
Round 2 - Top 4 of 8 move on, break all ties.
Round 3 - Top 2 of 4 move on, break all ties.
Round 4 - Championship, you already break ties for this.
Scores in previous rounds are disregarded.
You already break ties in the manner in which you list scores, so the proof of concept already exists. What do you think?