As https://lotro-wiki.com/index.php/Misty_Mountains_Quests points out, it's supposed to be an auto-bestow, and I could swear it always popped up. Now, however, I took a toon all the way up north to Helegrod to post the Evil Men warning, then back down into the West over to the chest, and the quest hasn't popped up.
Has anyone else had that problem recently?