In other games, pretty much any cups bigger than Go4 are 8/16 team invitationals, so biggest cups in TF2 probably should be solid 8 team invitationals (signups should not matter then). League format has always been the main way to play for non-professional teams in esports.
If maximizing signups for sponsors is high priority, one way is to add skill tiers and involve ETF2L more heavily. Their preseason cup with Open/Mid/High/Prem tiers got 90+ signups easily.
Edit: My point is that guilting players that don't participate in these cups is a bit scummy. There are multiple valid reasons for teams deciding not to participate (that may not seem obvious for prem players). If you want high numbers for sponsors, a single huge open cup probably isn't the way to do it. Don't hate the player, hate the game etc.
This is why I said signups do not matter for this tournament, because if that's your #1 metric for success, making the cup tierless, winner-takes-it-all qualifier for a LAN does not make ANY sense. It was almost tailor-made for low signups.