Travel into PNG from East Timor or anywhere nearby

Does anybody have any suggestion on getting from East Timor into PNG? We don't really want to fly via Australia or anywhere else because of cost - but all of the options seem to involve starting from somewhere other than where we are. We've thought about crossing over from West Papua, but it looks like we would end up a fair distance from the places that we think we might want to visit. Is it possible to get a boat from anywhere into Port Moresby?

If the option of going overland from West Papua to Vanimo doesn't appeal, flying via AU is really your only option.
There are no international passenger shipping services to Port Moresby from anywhere.

Darwin, in the north of Australia, would be your best transit option in Australia.