I reviewed the rules again, and one point is a bit confusing.
"The top 2 from each group advance; in case of a tie:
head-to-head record, personal encounter, date of the last game, coin toss."
Since the groups are small, with only 4 players, there's a high probability that if the 3rd and 4th place players both have 2 points, the head-to-head record and personal encounter won't help determine the top 2.
I suggest a small amendment:
head-to-head record
personal encounter
additional games (time will be added for them)
date of the last game

Changing the rules mid-tournament isn't ideal, but advancing solely because you played an opponent one day earlier also isn't ideal. If everyone agrees, I'll adjust this in the rules.