I touched on this in the other thread (about optimal strategies (https://paizo.com/threads/rzs43fkh?Optimal-Strategy-to-explore-Danger-Isla nd-and#1) for approaching the Danger Island book) 
But I wonder a bit about the timeline. My group just made it through the 1st dungeon, which is set up to take ~1 day (and certainly feels like a full days worth of activity and grants 3 / 10 feathers). 
That leaves you with 2 days and ~2 fights. (The optimization thread explains my thinking). I suppose that that's why the adventure length is 3 days? You probably want to have 2 fights, a few cool other scenes (watching other fights, friendly sparring with Tino's Toughest, introduce Lightkeepers) and then on to the next book.
And the big picture structure (where you could be challenged at any time) pushes groups to stay healthy and avoid conflict.
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Given length of the book available and the overall flow of the optimal play group that's probably right? Most groups kinda rush through, DM handwaves xp and you're on to the next book. It's a martial arts movie and you're just setting up the "serious contenders" for the "real tournament".
The whole place has a (fairly deliberate?) https://en.wikipedia.org/wiki/The_Isle_of_Dread vibe (the name, hexploration, etc). Also, really big monsters romping around and causing chaos is a sub-theme (which is expressed fully at the end of book 2).
There's also a shonen battlemanga thing where you have a lot of colorful antagonists to introduce. The ideal (though tricky) thing to do would be to feature most of the enemy teams at least once on the island.
They could seeing the enemy team 
-in a match or other challenge
-on the first scene on the beach
-in passing as they move around the island
-challenging the enforcers?
I tend toward more simulationist/completest vibes, I like option-ful sandboxes for PCs to explore and I'd like to see the PCs get a chance to explore the island.
Also it would be nice to have some ups and downs. Maybe the PCs don't win every battle? If the Lightkeepers get their last feather off the PCs and they have to catch up to advance it's probably set them up nicely as rivals?
(I'm not usually particularly heavy handed, but that kind of thing seems like it would increase tension). 
I'm thinking about making the tournament time longer? Maybe a week?
(In my game I'd probably actually handwave it a bit but I realize some groups probably don't go for that style of play).