[Dain]

That is strange, because the two passages seem to disagree: mine seems to say he went south when he disappears, but yours seems to indicate he scouted around mordor and then to Lorien. Maybe he went south after that, as there seems to be 20 years between then and when Gandalf asks him to help him (3001), from which point he seems to be helping Gandalf more directly and hunting Gollum (though he doesn't catch him until he's released from Mordor 3017). Interesting!