Although we didn’t go there, you can also use Jayapura/Sentani as a gateway to Wamena and Lake Habema. This does add quite a bit to your budget as there doesn’t seem to be any cheap way to do it which is the reason we didn’t go there.
Trigana Air flies there several times a day but they only show schedules on their website, you can’t book online. From what I could see online, you will need to have a local travel agency arrange your guide, porters and transport. Burung Nusantara has some information and recommendations for guides and travel agencies. Since I didn’t go there, I can’t speak as to the quality of the services but there are links to birding trip reports on their website. You will need to have this area mentioned on your Surat Jalan along with Nimbokrang and anywhere else in West Papua you plan to visit.
If you do make it there, the birds are amazing! Burung Nusantara shows the highlights as: Salvadori’s Teal; Snow Mountain Quail; Chestnut Forest-Rail; Dusky Woodcock; Goldie’s Lorikeet; Mountain Kingfisher; Macgregor’s Honeyeater; Crested Satinbird; Papuan Grassbird; Greater Ground-Robin; Lesser Ground-Robin; Alpine Robin; Wattled Ploughbill; Northern Logrunner; Papuan Whipbird; Blue-capped Ifrita; Torrent-Lark; Splendid Astrapia; King-of-Saxony Bird-of-paradise; Superb Bird-of-Paradise; Brown Sicklebill; Lesser Melampitta; Archbold’s Bowerbird; Alpine Pipit; Mountain Firetail; Snow Mountain Munia.
I would add the Tiger Parrots to that list!