March 2017 - last edited March 2017
According to this Gamefaqs thread (https://www.gamefaqs.com/boards/920668-dragon-age-origins/57442930), this is caused by having too many items in your inventory. Exactly how many it takes to trigger the bug is unclear, but it is somewhere greater than 125 (the normal maximum possible inventory without using mods, console commands, toolset save file editing/etc.) and less than (speaking from personal experience) 1165. This problem is unique to Golems of Amgarrak - neither Awakening (importing from Origins) nor Witch Hunt have this problem.
EDIT: i have tried loading various saves from my Origins playthrough. Saves up to and including my "Camp - Edngame" save (869 items in inventory, 811 when imported into GoA; in camp, after landsmeet but before final battle sequence) work just fine, but my next save (denerim palace district, 907 items in origins, 841 imported to GoA) and anything after, including all of my exsting Awakening saves for that character, load into the closed room. Also, I noticed that when I load into the closed room, I get a "new item" message, but no new item in inventory.
When loading GoA properly, some new items are received - assorted high-level health potions and "Memories of the first warden". When loading into the closed room, a "new items" message appears but the items above, or any other new items, do not appear in inventory.
Dumping lots of low level items (old armor/weapons, nothing from other categories) from Palace District endgame save (new inventory count 800 in Origins, 758 in GoA) loads properly.
Dumping lots of items (again, old armor/weapons only) from Awakening final save (new inventory count 778 in Awakening) still loads into the closed room.
Update: Dumping every last generic weapon and armor item in inventory, and a few low level mage hoods, reduced my Awakening endgame save to 607 items. This save then imported and loaded properly into GoA.