It’s not easy, so I’m just going to throw out some ideas. Maybe checking for airplane mode in the beginning? Taking the time to check for airplane mode once, even if it's only in the beginning, might be enough to scare teams planning on cheating.
The auditorium setup probably made it harder for you guys to see our screens. If its something under your control, maybe try a room where everyone sits level? This might make it easier to see everyone at once, so you guys could stay more or less in the same area for the entire exam. Walking around can give teams opportunities to look something up when a supervisor is the other side of the room, but staying in one place and being able to see everyone's screens makes it more difficult to cheat.
Another strategy could be to seat teams a tiny bit closer - not too close that they can easily see each others screens or hear what others teams are whispering, but enough to make cheating appear riskier. Again, this would also make it easier to see everyone’s screen at once. The right distance would be tough to figure out though.
I talked to my partner, who was a bit more aware of his surroundings during the test, and he said you guys did a better job than most supervisors at other invitationals when checking screens. I wouldn’t worry too much about it - just maintain the same test quality you guys had, and Astro should continue to run smoothly.
I'm not sure that cheating is a gigantic concern at invitationals and I think you're overthinking this - I've encountered two reported cases of suspected cheating on my team's behalf. One of them turned out to be completely baseless, and another one was because our people did so well
NJSO thought the proctor (one of our HS teachers) had passed on the exam key to our competitors.
There's really not much incentive to cheat, and certainly not among most of the schools I've competed with and against. A simple check once at the beginning and occasional monitoring should be sufficient.
This matches with my experience. Instances of actual cheating are exceedingly rare.
No one should be cheating anyways. I hope that everyone is following the Science Olympiad Pledge
I pledge to put forth my best effort in the Science Olympiad tournament and to uphold the principles of honest competition. In my events, I will compete with integrity, respect, and sportsmanship towards my fellow competitors. I will display courtesy towards Event Supervisors and Tournament Personnel. My actions will exemplify the proud spirit of my school, team, and state.