While it provides no solution to your problem, I purchased the physical CE edition through Gamestop, and all codes worked perfectly. Whatever the problem is, it's not affecting ALL physical Gamestop purchases.
Early access code worked fine. Received my CE box last week, opened it up, found the code in the Heavensward disc case, and plugged it into the Playstation Store's code redemption area. The next time I started FFXIV, there was some downloading and stuff, and everything's worked fine since.