Possibly because I had previously cleared Haknir's Shoal, when I returned there after reaching the required level 36, I was able to loot the Map off the dead pirate captain. That began the quest. But the Ancient Chest was not there, and the place where it should have been was a mound of snow instead of a sunken dig. I tried running away and coming back, but it didn't change. I explored other nearby islands just in case I was somehow on the wrong one, but it was definitely the right one and when I returned to it, still just a mound of snow. Finally I fast-traveled away, and then back again. I don't know if this is related, but when I returned via fast-travel it was night time, instead of day, and snowing fiercely. The shoal was completely different: the pirates had respawned, the snow mound was gone and in it's place was the sunken dig with my Ancient Chest. I re-killed the pirates, looted the treasure map a second time (although it still only appeared once in inventory), and retrieved the Deathbrand Helm from the chest. From there I had no trouble completing the rest of the quest.
So, if you arrive on the shoal and there's just a snow hill between the three rocks, try leaving and returning via fast travel, and possibly try returning at night. Best of luck to all brave adventurers.