If something like this were to be given the go ahead then I doubt time zones would be much of a factor when it came to tournaments being completed.
All that it needs is a time and date of when the tournament will be played and people apply to be a part of it based on their availability.
Whether one or two players showed up wouldn't make much difference, the game would be played either way.
This is assuming it's a one off game where all players compete in the same match.
Set up a separate part to the forums, much like the reports. Players link their in game accounts to the site. They input their timezone, which cannot be changed after initial registration, without the approval of a staff member.
Tournaments are then available to view, clearly stating all details. If someone was to register for a tournament that starts at 20:00 GMT and their time zone is GMT+6 then a warning message would pop up before completing registration confirming the user is aware that this tournament will be starting at 02:00.
With regards to prizes, I think giving out ranks should be only for special tournaments, like Christmas, Halloween etc.
Prizes could instead be vanity items, special tournament hats/trails/miniatures. Even special point multipliers to activate on the server.
The current community tournaments are hit and miss whether they'll be a success, some people just can't be bothered with continuing and don't bother telling anyone or completely forget about it. It's also limited to forum users.
With official tournaments these could be advertised throughout the server leading to more interest in them, and would be a lot more organised than the current ones.
TLDR: There's no reason why time zones should create difficulties for this, a bit of organisation and Bob's your uncle.