Hrqls: I hadn't thought of the random game type tournaments. I can think of a few ways.

One way would be to seed them randomly!

Another way depends on how the actual game to be played first is chosen. Does everyone in the tournament play the same game in the first round? If so, after the game is chosen the players could be ranked and seeded by the rating they have in that game. For the second round, you could re-seed the field or keep it as is.

A third way would be for the games to be played to be picked for each round in advance and then the total rating to be used for the seeding. Whether or not the game order is revealed to players if it is done this way would be up to the tournament creator.

I'm sure some other ways can be thought up. I like the second way that I just made up of these three ideas. Allowing the tournament to be started after the deadline with a pared down list could also be done. Say you have a 32 player tournament, but only 21 sign up by the deadline. Even after the deadline is extended it is still 21 entrants, start the tournament with the top 16 seeds. Yes, the ranking and seeding of them is a problem for a random game, but idea number two would work for that too.