Maybe you could do a more passive approach. Something like posting the trivia somewhere (even a pastebin could do) and people could reply on the site the whole day, or if you're confident about the harshness of your trivia, you could even give a whole week.
That's a bit too open to cheating, looking up a faq or wikia could get you any answer you need really, no matter how I word the question. It wouldn't matter if I wasn't giving out a prize, but I don't want to reward the person who has the best Google-fu skills.
Getting it set up will be the hard part, but it'll work out. Obviously not everyone can participate due to these things called timezones, but if people do want to take part I don't think it would be hard to find an hour to put aside on a Saturday every couple of weeks.
I plan on making it as easy as possible. I'll be sending out reminders to everyone who shows an interest, with links and such to the Mibbit I'll set up so people can just click and join easily.
It boggles the mind
The world man. It just keeps on a turning
You're high again, aren't you.