Does anyone know why they claimed only half? I mean, even with claiming half the island they still only had a few scattered trade posts around the coast so why not just claim the whole island?
I'd actually argue that it would be due to the Dutch not having any need for the eastern half of the island. It wasn't until the second half of the 19th century that the Dutch managed to completely control their East Indies colonies. Most of the initial possessions on the island were small coastal ports. The inland push didn't occur until later, and the colonial borders are an afterthought to what is most important: possession of the ports. The land in the middle is chump change compared to the coastal possessions.
Speculating, the Dutch likely established ports throughout the region to expand their spice trade, among other resource extraction in the region, while also eliminating as much of the potential for competition within Indonesia as possible. As such, the western expanse of the island, being in the general vicinity and having been colonized by similar people, fell into the Dutch sphere.
In comparison, possession of the eastern expanse of the island would only be practical as a projection of power into the Pacific itself: the various ports have little bearing for the core of the Dutch East Indies, but instead would serve as ancillary ports of call on a route to expansion in the east. See the British in Southeast New Guinea, which straddles Australia and their Pacific island protectorates/colonies in what is now Kiribati, and the Germans in Northeast New Guinea, which was a colonial claim by a nation that was picking through the leftover remnants throughout the world. (It also served as a good anchor for German Micronesia as well).
So, to make the Dutch desire the eastern half of New Guinea, it shouldn't fall down to the Dutch being stronger. It needs to fall under the Dutch needing an eastern, Pacific facing port in addition to the western ports that face their colonial jewel. (Note that OTL this wasn't needed; the coast was the important part, and the jungle was practically impenetrable until much later. There is no threat of losing the ports by land). Eastern New Guinea isn't necessary for complete control of the Indonesian littoral, it is needed to connect the Dutch with any feasible colonies that are in the Pacific.
I would propose that the PoD start with the Dutch maintaining one of their colonies in Oceania. Van Dieman's Land, Nieuw Zeeland, etc. That way, you have the purpose for ports to be established on the eastern side of the island, especially in a time before steam and telegraph becomes a thing. You don't need Australia in total for this, but the addition of the other territories to the Dutch East Indies would give a practical reason for the establishment of ports along the island. By the time that territorial boundaries are drawn, the ownership of pretty much the entire littoral would end up making the island united, de facto. (This doesn't mean that the islands nearby would also be united with New Guinea. Same reasoning applies, especially if the more southerly route is the one needed.)