I think the new format is better.
I would suggest if using 6 games then everyone plays the 6 games 1 time and then has 4 more SINGLE attempts to better their scores.
This means every game counts, but they can still better a bad one or blow all 4 on that one game that eludes them for a good one.
Then focus your energy and extra time on playoffs.
We run our monthlies with everybody plays 1 time through all available games for qualifying and that puts you in a specific 4 pack. You can not do better or worse than the 4 pack you qualify into. i.e. qualify 7th and you are in the 5-8 playoff pack with best position being 5th for the night.
This puts emphasis on every game played and still gets things done in ~3hrs with ~20 people.