Ahem. You’re missing Phoenix and Cerberus on your list (the South Island conventions).
For Cerberus (I’m on the organizing committee) and similarly for the other conventions - although I don’t know their specific behind-the-scenes actions - we have a “Shark Week” where people sign up for the games they want in each round, ordered by preference. At the end of that week everyone is assigned to their first pick in every game, and from there if any game is oversubscribed we (in Cerberus’ case) manually shift people (at random) into their 2nd choice game. This is repeated until no games are oversubscribed.
There is a very strong rule that no-one gets two “2nd picks” while anyone on the list still has all of their first picks. So far this has not been an issue*, and typically it will only be 20-30% of people who have any second picks on their allocated games at all.
After Shark Week game picks are processed in the order they come; that is to say players are placed in their games as soon as they sign up. Preference here again is to (obviously) give them their first choice games, but if they choose a game that is already full, they are placed in their second choices. Here, it is possible to get more than one 2nd pick, as we will not move players that registered in Shark Week out of their first choice games in favour of someone who signs up later.
* This year unfortunately was a bit of an exception, as we had to cancel three games due to lack of player numbers. The games that were cancelled were the ones that had the least number of signups but inevitably they were the 1st pick of those players, so if I recall correctly there were some players this year that did have more than one 2nd pick, but that was because the games they picked were cancelled, not because we wanted to give them that many 2nd picks. There was quite a lot of wailing and gnashing of teeth on behalf of the organisers when this happened, particularly with regard to one player who had selected all three cancelled games