AHC: Belgian Solomon Islands

This is a piece of history I read about the islands:
Missionaries began visiting the Solomons in the mid-19th century. They made little progress at first, because "blackbirding" (the often brutal recruitment or kidnapping of labourers for the sugar plantations in Queensland and Fiji) led to a series of reprisals and massacres. The evils of the labour trade prompted the United Kingdom to declare a protectorate over the southern Solomons in June 1893.
In 1898 and 1899, more outlying islands were added to the protectorate; in 1900 the remainder of the archipelago, an area previously under German jurisdiction, was transferred to British administration apart from the islands of Buka and Bougainville, which remained under German administration as part of German New Guinea. Traditional trade and social intercourse between the western Solomon Islands of Mono and Alu (the Shortlands) and the traditional societies in the south of Bougainville, however, continued without hindrance.
So what if for some reason the Belgians would be first to land on the islands? Or think of another reason to make them Belgian.
What would happen? How would the islands be administered? Would Belgium be able to keep hold of them? What effects would there be on world history? Would it become a first step for a bigger, albeit late, Belgian 'empire'?
 
This is a piece of history I read about the islands:

So what if for some reason the Belgians would be first to land on the islands? Or think of another reason to make them Belgian.
What would happen? How would the islands be administered? Would Belgium be able to keep hold of them? What effects would there be on world history? Would it become a first step for a bigger, albeit late, Belgian 'empire'?

Leopold II of Belgium (he of Congolese cruelty fame) originally tried to buy some colony from the Spaniards - though I think that it was the Philippines (can't remember) - during the late reign of his father or his own early reign. I can't remember if Parliament wouldn't give him the funds or what the reason was that he couldn't close the deal, but he was already driven by the urge to imitate Badouin of Flanders, Emperor of Constantinople, Comte de Hainaut et de Flandres and other great Crusader Belgian figures.
 
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