You know, I have suspicion that the event could be not entirely random, but instead hardcoded into the game...
A few times I had the first wave in playthrough – immediately taking me to that island...
But if I skipped that 1'st wave – I couldn't get to the island after dozens of more tries... 🙄
Dunno, only the gamedev would know for sure, but it's just my hypothesis – that there could be some scripting involved.
I have a new game save still around, and can double-check that...
But in any case, that 3'rd island is so obscure, I didn't know if even existed for like good 4 years replaying this game time after time, since 2021.
So, if you'll get there, you'd be among the elite. 👧🏻🏆