Spoiler for Pointing out the problems:
Three things to note
1. My interent is very limited
2. So is gino
Interest or internet? If people don't participate because of low interest, I don't think we should wait for them. If it's about limited internet, what form of limit are we talking about? Do you mean laggy internet that doesn't load Pokemon Showdown or that you can only access good internet at specific times? If it's the first, then what good can waiting do anyway, and if it's the latter, it's all a matter of finding a good time for both players.
3. The timer is not a "do it or die" thing. I'd like to keep things hastened but that's not a huge priority, as I've said extentions will be given freely and openly. No sense in forfeiting a fun friendly game ^^ the original even offers three full weeks, consider that your ceiling for extensions
If my memory serves right, the original event died because of extensions. It's not fun and not a game if nothing is happening and it makes people lose interest.
About full week extensions, the only reason we should do that is if someone is only available at a certain time of every week, but they had something scheduled for that part of the week already. For these players, they need to cram 4 duels + teambuilding time into that time of the week, every week. That might be impossible to do, unless an unreasonable time would be given, which would be unfair for everyone else.
I agree with the idea of extending the tournament to allow for people with poor internet, or those in very different 
zones from their opponents (like me and ji412jo for example). But if this is going to be the first round of many then 3 more weeks might be a little excessive
Indeed 3 weeks is insanely long for a single round. That almost guarantees a dying event. I'd say 3 days maximum is bearable, 4-7 days comes with mild interest loss and anything beyond that is death.
This is usually a 3 round max tournament, but honestly, it doesn't /have/ to be a tournament. After this game series is done we could move onto a league format like BL or CL (though, it would have to refresh monthly to allow new types) Really, im not sure how I want this to proceed (after this tournemnt), if anyone has any ideas I welcome them
Considering what the goal is, there's an idea. We don't need to cut everything into rounds, because in the end, everyone has to duel everyone anyways. If we are allowed to challenge any player at any time, we can maximize efficiency and we only require one, final deadline, which can be given flexible extensions if needed. We should still keep "rounds" as an index of who should we challenge next and as a reminder that we should duel them if we see them online. (Players can easily forget who else is playing)
Another advantage of this would be that players wouldn’t need to duel everyone. Just like in Pokémon, if you wanna be the very best, you win more if you duel more. You don’t have to, but in the end, people with more wins get more points. People who didn't play enough games probably won't place high, but at least they were given the opportunity to play against everyone.
Alternatively, keep the rounds and stick to deadlines, BUT for those players who failed to finish their matches, let them carry their matches to the next rounds, essentially stacking responsibilities for later. This would keep the games flowing and also allow for some flexibility.
