I have a similar issue. I completed all the requisite quests years ago, and I confirmed they're in my completed quests log. I can access the second floor of my mog house in my home nation, but I have no option to select Mog Safe II when I talk to my moogle. My options, from top to bottom, are Mog Safe, Storage, Mog Locker, etc- no Mog Safe II. I am not 100% sure, but I believe I did have access to the second storage right after the update.

I've tried zoning, rebooting, etc. All the obvious things. Nothing fixes it.