From my e reader, so I cannot do live links, please accept my apologies.
Have you contacted the Salvation Army to ask what types of searches they would have done back in earlier times, would they have : put notices in newspapers/ door knocked/checked directories /written letters etc ?
Have you looked at Trove from the point of view of looking for Salvation Army adverts looking for him?
I have NSW offline resources, including some early Electoral Rolls. Some of these are hardcopy, and some are on CD. All are pre WWI. I will not be able to access these for around one week, but after that .... well .... (cannot do smiles from the e reader either)
The NSW BDM index does have flaws ... eg while d.c.s post 1856 are full of detail (depending on the knowledge of the informant as Neil mentioned) they do incorporate burial details, including cemetery, clergy, funeral directors, the INDEXES do not include deaths where no registration was made. So, it is possible that if a death occurred which resulted in an inquest, that that very process did not automatically result in the registration of the death. (It was not clear from the admin processes who was expressly responsible for that type of registration ... the coroner/the funeral director/the clergy. Many/most coroner's inquests re deaths were registered, but not all). Sadly there are also deaths for persons whose name was not known.
The information on early Electoral Rolls (and current ones too) does not expressly confirm all the members of any one household, so they are not as helpful as say a Census report, but they are very good pointers. They are by electorate, and then by polling place within that electorate, and then by alpha surname, and from c1902 .... for males and females aged 21 and over. etc.
Sorry I cannot immediately help, but if your chap hasn't turned up in a week or so, I will try to help then.
Cheers, JM (still mastering the tiny e reader keyboard, but lots less typos than my first efforts from it)