Rachel, here are some notes based on my experience with double regionals in Minnesota that might be useful in thinking about your super-district proposal. Our local committee presents two double regionals, each with 124 teams participating.
The regionals in Duluth are held in the
DECC arena (curtain between the two events), with the pits in the attached two convention center spaces. We use the arena and the two convention spaces in the lower right hand part of that map. One of the two regionals is space constrained, based on the square footage available in the City Side facility, which limits us to 60 teams in that regional.
The regionals in Minneapolis are held in adjacent facilities. 10000 Lakes is held in Williams Arena, which has an attached Sports Pavilion that can accommodate 64 pits. Across the street, North Star is held in Mariucci Arena on the arena floor. That regional accommodates 60 teams and is very tight space-wise.
The football stadium is probably the only facility that could accommodate a 200 team event. It's possible that it could be held in the convention center, with a scaffolding grandstand for the field.
Regardless, at 200 teams it would probably be a four field event. It would be about twice the size of event that we currently staff with volunteers, so you'd need some transition strategy to build up the volunteer base for the event. I'm not aware of any local committee (run almost entirely on volunteers) presenting competition events larger than 124 teams. IIRC the next largest local event is FiM, with 102 teams this year.