Reasons colonists might want to conquer the islands:
Spices are typically found in tropical environments. Spices are also tremendously valuable and always in high demand.
Slaves. Goblins may not have the raw strength and endurance of other races, but they have tiny deft little hands which would be good for textile work (another huge pre-modern industry). They are also used to being bullied around. Slavers add moral ambiguity to the game, which seems like something you wanted to avoid.
A land crunch back home means that there are very few opportunities for people to raise their station. Going overseas become the only way to make a name for ones self.
The islands could be strategically located. Holding the islands gives control of the sea between home and some other greater source of wealth & power and also denies the same to hostile powers.
More random ideas:
A Sargasso Sea type area controlled by hostile aquatic treants, who resemble enormous clumps of humanoid kelp. Or maybe just palm tree shaped treants are exotic enough.
Psionic attack monkeys. Maybe I played too much System Shock 2.
A volcano tall enough to be snow capped year round where fire and frost giants wage unceasing war upon each other.
A cult of weresharks, who use a powerful magical ritual to turn freshwater ponds, springs and rivers into undrinkable brine.
Aaracokra could find a happy home in this setting. Gliding from island to island on warm tropical breezes. They’d make great scouts and lookouts for ships.
An errant iceburg floats thru the island chain. The locals view it as a terrible omen. But in reality it is a Sliver Dragon trapped in an icy prison.
A goblin shaman uses a captured ship and a crew of lacedons to raid and plunder.
