I don't think you're in the minority on liking the concept of Bullseye. Doing some akin to "Bert's Family Feud" and its system of rewarding number one answers on the first pass through Fast Money would be the best, even if I don't like that version of the show overall. I was originally for something about number ones in the main game like Adam is, but realized that can reward teams unfairly that take more time getting to 300.
I was really down on the sped-up single/double/triple format until I watched a couple of Dawson '94 shows about a year ago. They had a little more time to have fun on that particular version, so it wasn't so noticeable. I can't remember a single time where it seemed Ray had ample time to compete with Bullseye.
But anyway, that rushed format isn't so bad if you view it like it were Password Plus' scoring. The eventual point totals of the questions were so routine, you can call the first two questions the "$100 puzzles" and the last two "$200 puzzles" in that if a team gets the first two, the other team needs the third to "tie the match" and go to the fourth question "tiebreaker." If they split the first two questions, then it comes down to the third, a'la the $200 puzzle in those situations on P+. Not perfect, but not horrible either.
-Jason