The only times anyone would "monkey" with the switch was when it dropped ALL traffic for them, NOT just the internet or inter-table but everything including same table CIFS transfers were cutting out. And that individual wasn't the only one affected by the intermittent disconnections, I had my system cut out multiple times, so did OP, and everyone at the table. The problem might have been a hardware/configuration issue in your switch, or maybe the 10+ year old geriatric switch had some other issue that caused it to have a mini-stroke and crap its pants every ~5 minutes.
Just curious but were you using the cable modem for DHCP?
On the subject of tournaments, I really don't think the group that is running the event should be playing in the tournaments. Seems kind of a conflict of interest in that you're team is organizing, judging, and scoring events that its capable of winning trophies and/or prizes from. Also, the tournament/competition information needs to be more visible. Try putting upcoming start times and the current time on a screen or a projection near the exit.