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I'm in favor of 16 groups of 4 players each.
There isn't much time for the group stage – each player has 3 games in their group.
Each player will have at least 3 games.
Pasha, I didn't understand the issue about players not making it out of the group? If several players have the same number of points, there's the Berger coefficient, head-to-head results, and who finished all the games faster – we already have experience with this in tournaments.
Then, from the round of 16, it's an Olympic-style bracket.
In my opinion, this is a good option.