So, according to the FAQs:

(1.14) The word “cannot” If a card effect uses the word “cannot”, then it is an absolute: that effect cannot be overridden by other effects.

In the Road Darkens, Doom, Doom, Doom says: "Forced: At the end of the quest phase, remove 1 damage token from Doom, Doom, Doom. Then, if there are no damage tokens here, add The Balrog to the staging area."

Now, when I played through the scenario, the final damage marker was removed in a means other than through Doom, Doom, Doom's text - I believe it was a Moria Orc. So, technically, does this mean that since the first half of Doom, Doom, Doom's text could no longer resolve successfully (you can't remove a damage token), that the second half (where the Balrog comes and smashes you) can no longer resolve?

I'm assuming you meant to reference this:

(1.15) The word “then”
If a card effect uses the word “then,” then the preceding effect must resolve successfully for the subsequent dependent effect to resolve.

I think you might be technically right, although I'm sure that was not the intent.

Edit: Looks like this has come up before: https://community.fantasyflightgames.com/topic/134548-doom-doom-doom-card-from-the-road-darkens-official-errata/

Sure enough, looks like there will be an errata to correct it in the future. (As a note, I did have him appear - didn't notice this until later when I was skimming over the FAQs.)

It is a little odd that this wasn't included in the FAQ they just published. Maybe the Q wasn't AF enough to make it into the official record.

You can also quest like hell and finish before the balrog arrives!