I've played the Passage to Mirkwood quest in the neighborhood of 10-20 times, and whether or not the game I just finished counts as a win depends on one rule interpretation that I think I handled correctly, but am not 100% sure.

The situation:

Aragorn is readied, waiting to block an attack. Another enemy's attack undefended attack on Gloin is resolved first, and the shadow card requires me to exhaust two character cards. Gloin gets hit, and Aragorn gets exhausted because of this shadow card.

Aragorn was originally slated to block an upcoming attack from Ungoliant's Spawn, which would have hurt him, but being defended, it was survivable. So, because Aragorn was now exhausted, the attack was undefended. Here's where the murky part comes in for me: Because the attack by U.S. was now undefended, it seemed to me that I would treat it like any other undefended attack and assign that damage to Gloin, rather than Aragorn, the character who was originally slated to block U.S. but now was exhausted.

Long story short, Gloin dies, Aragorn lives, he and Glorfindel help me in the next few rounds polish off Ungoliant's Spawn, and (maybe) win my first game.

Did I handle that rule correctly? Should there be much rejoicing throughout the land or more banging of my head against the nearest wall?

Yes. If an attack is undefended you can assign the damage to any of your heroes*. In any case, as far as the game state is concerned, there is no such thing as being 'slated to block' an enemy. Deciding that a certain character will handle the defence is part of your own forward planning and has no effect on the game until you actually enact it by declaring them as the defender.

* Actually in some later scen arios there are exceptions to this when an encounter card effect states that an enemy attacks a specific character, but in general it's true, and these exceptions are a long way from Passage Through Mirkwood.

Thanks for the clarification. Now to celebrate by getting absolutely destroyed by Journey Down the Anduin!