So less than 24 hours in and I have a dozen replies and there's plenty of people who liked my post and didn't enter the form. Thanks for the input! Just a few notes -
Almost everyone who replied was fine with either, but a few showed preference to a more normal tournament over a gimmick tournament. That would lead me to want to run something without any gimmick rules... but someone did reply with an idea that seemed interesting to me. Maybe a bit hard but something that I could end up exploring is giving teams a secondary way to "win." There are a lot of Jackbox games that do this for those of you who have played those, but just as an example - maybe giving props to the team that had the most close sets who didn't end up winning, maybe giving props to the team that got snubbed by a particularly difficult bracket or things like that. Obviously it's not as good as actually winning the tournament but still.
Not everyone who replied to the form gave me the times of day that work best for them, but a majority of the people that did seem to be fine working with something in the general area of 5 PM - 10 PM EST. I haven't tried to check for anything more specific. In hindsight I probably should've asked two specific questions there for both weekends and weekdays just to be sure. As it stands though I've played with people from EU enough to know that this is super late for them and might also be a bit awkward for people in west coast NA time zones if it ends up being the later parts of that.
If you're not on a team then I'll probably be taking DMs so people could sign up as individuals and I could try pairing them together some amount of time ahead of the tournament starting, so if you're not on a team, don't worry. A few people have asked where I plan to host this and I'd want to look into my options. Battlefy and Sendou are the most probable ones, leaning towards the latter since it's easier to make an account for and I know there are a lot of people here who haven't joined any tournaments yet so there's no guarantee they have an account for either.
I would make it a priority that everyone plays as many matches as possible rather than it being just one double elimination bracket like some tournaments are for other games. Would probably end up being swiss/rr with results from that placing each team into an elimination bracket, although I'm not yet sure how I'd accommodate for the possibility of the tournament either having a lot of teams sign up or very few teams sign up.
Lastly, someone mentioned me trying to look into getting a Sendou badge. For those of you who don't know what that is, don't worry about it, but I didn't think about this at all before. Part of my concern is that there are A LOT of people who answered this form who have never done a tournament before and the kinds of people a Sendou badge would attract are likely decently high level players. I technically wouldn't know that for sure, probably is something I could ask more experienced TOs (which I should mention - I will be asking at least one for help before I do anything here). I would skillcap the tournament but that could introduce some other problems if some people here would just get screwed by that. Maybe this isn't an issue because the ways I mentioned I'd set up the tournament would mitigate the problem, I dunno.
So, yeah. Lots to think about before I want to dive into something like this. There's more I could say but I don't want to make this post too long. Thank you all for the feedback so far! If you have anything else to add then feel free to either send me a message or just fill out the form again if you want. Doesn't matter to me either way.