Kadaj...Chu's BRAWL Biweeklies are quite possibly the worst examples of how long Melee tournaments take.
To keep it short:
-mad delay on startup time because Chu is nice about late people
-like...3 Melee setups >_>
-people being dumb about playing tourney matches as quickly as possible
I've got faith in these TOs though. It could definitely be done. I doubt I can make it but if I could, I'd love to help out ^_^
Back to being able to do this: the absolute safest thing to do would be to say you can only enter one or the other [Brawl teams/singles or Melee Singles] and I'm pretty sure I already saw them mention that as a possible rule.
I've tried running both events simultaneously and time becomes a huge issue when you have players [especially teams] who are running through the winners/losers bracket in BOTH games simultaneously. Also, most players won't want to go from one game immediately to the other, esp when they have a winning streak.
Just my experience with it...
In the end, the TOs do as much as they can to encourage people but it falls on the community to provide enough dedicated setups for each game in order for this to function well. [Don't forget powerstrips, either >_>]