I think that I have found a perfectly entertaining solution.

Nobody goes home until Sunday evening. The full field plays all rounds until all golfers are sorted from 1st place down to 64th place.

Example: In a field of just 8 golfers, it would work like this:

The winners of the first match will end up in one group, that will make up places 1-4. The losers of the first match will end up in another group, that will make up places 5-8.

The winners of the first match that won their second match will fight for place 1-2. The winners of the first match that lost their second match will fight for place 3-4. The losers of the first match that won their second match will fight for place 5-6. The losers of the first match that lost their second match will fight for place 7-8.

At the end of this eight-player tournament everyone will have their unique place in the tournament results:

1 WWW
2 WWL
3 WLW
4 WLL
5 LWW
6 LWL
7 LLW
8 LLL

Why does this make the tournament more interesting to watch? Because while the undefeated twosome tees off to decide the tournament winner, the worst two performers of the week will be in a hard-fought battle to come in 63rd, i.e not last. You bet that that will be a good, hard-fought match! Especially because 64th place gets no prize money. Besides that entertainment, there should be at least a few other matches on the course that might be worth watching, for whatever reason.