Okay. I don't give a skeever tail about having the item, but I do care about finishing the quest.
I hadn't bothered to do the Thieves' Guild quests for quite a while after initially joining (and promptly selling the armor) back at the 30 hours of gameplay mark. At about 160 hours of gameplay I went back to go finish up the thieves guild quests and wrap up gathering the very last of the stones. After all that work and all that collecting, the armor I sold about 110 play hours earlier is stopping me from completing my last achievement.
Is there any workaround that works on the Xbox 360 and does not involve going back 100+ gameplay hours?