You have it similar to how I'd run it, except for a few tweaks.
Have 3 players only be able to qualify, using the fastest WC time method. My big difference is, that, given there would be 2 games in a half hour, the first game can pit players A and B (the two fastest), for example. The winner, say A, would play the WC, and if lost, would play in the game's 2nd half, which would have A vs C, while B sits out until the next game. The winner of A vs C would go to the WC, and if not won, would play against player B at the start of the next episode. I would set a one week time limit for the WC to be won, before the opportunity is lost (or as an alternative: the million could carry over to the next tourney, with 2 million at stake, with the biggest WC consolation money winner for the tourney week being invited back, and only 2 normal players eligible from the next 10 weeks to play).
This way, I think it would be harder to get into the tourney, there would be no more coin flips, and each of the 3 players would get to play on a daily basis, meaning no more what I call "lucky shot" days, where the one sitting out doesn't have the chance to take on the prior day's winner, who has "momentum" going, and possibly somewhat of an unfair disadvantage. It also helps the players sitting out to not lose some of their own "momentum"...
