Appeals Committee. Disputed situations in tournaments.

Sorry, Pete, but you're also wrong here. If one of the players doesn't want to play, it's unpleasant for them (for various reasons), they won't play, no matter if you give them a month or a year for the game. If their opponent wants to play, it won't be you bothering them, but they will bother you, saying that the opponent is avoiding the game.
But if both opponents don't want to play, you won't achieve anything.

You should have simply given both opponents a technical defeat at the end of the round, as a matter of course.
Firstly, you won't waste your nerves and energy, and believe me, they are not unlimited.
Secondly, you won't bother the players unnecessarily; they also have nerves, because it's obvious that the rules have been violated – there's no reason to understand the fuss on the forum.

Alex R, Vigo, and Vitalik are well-known players, but in the tournament, they are equal to the others, and the rules are written for them too. In fact, you did everything right, well done, but a single phrase about the rules would have been enough.
The player needs to show initiative during the round, not after.

Friends, we are slowly sinking into a swamp of disputes and petty squabbles, and they are not worth it. We have a forum where you can chat, we have a Community of players, quite friendly, where you can always find an opponent for your favorite game... what else do we need?