I don't think it helps to view the up as having its own denotation here. The meaning of end up is certainly related to the meanings of various other verb-particle idioms with up (such as wind up: "we wound up talking for hours"; and turn up: "he turned up missing"), but ultimately, they are idioms, and best viewed as complete wholes.
Syntactically, too, it is end up + <adverbial>, not end + up <adverbial>; for example, one can say "Where did he end up?", but never *"Up where did he end?"
The opposite of end up, incidentally, is start out: "he started out in the Army". It works much the same way.