So I entered Galawain's Maw, and started exploring the area, without having received the quest yet. I went north-east by crossing the broken bridge with a grappling hook, and then pushed on in the same direction until I met the wall of brambles, which I also managed to get past with a skill check.

 

So I found Sul and Irensi, and killed both after trying to come to reason with them (well, I did suggest the Bear was a more legitimate candidate, and they didn't take it well).

 

So as soon as I did, my journal created the quest entry and updated it to the phase "Return to Desthwn at the front of Galawain's Maw: I've resolved the stalemate between the beasts. Desthwn will want to know the outcome.", and I was shown a brief cutscene showing the bear and his attendants emerging from a dark passage in the north-west. I then explored and cleared the rest of the dungeon, killed all remaining lions, and made my way back to the front of the Maw.

 

Only, when I talk to Desthwn, noe of the dialogue options allow me to progress the quest any further, all leading to Desthwn asking me if I have sorted things out yet, with me only being able to reply "still on it"...

 

Anything I can do to sort this out?

I just encountered a similar issue.  I actually did the resolution before even getting the actual quest from Desthwn.  After my journal updated and told me to go back to him, I don't get any new dialogue options to progress.  I did find it quite odd that I was doing what appeared to be a quest, but once finished had me scracthing my head at what the point of that was.  Then I find the quest giver...

 

Fortunately, a five minute autosave reload fixed this issue.

Edited April 26, 201510 yr by Sanctuary