I found a solution elsewhere which I tried and seemed to work for me when nothing else did.
Solution: Move all the game files (core game, DLC) onto the internal xbox drive and UNPLUG any external drives you have.
My scenario:
Originally I think I installed BF4 on an external drive, but later on I noticed that some DLCs ended up getting installed on the internal or a second external drive I had. So I made the decision to group them all together all onto the same external drive that the original game was on. I don't think it was long after this that I noticed Dragon Teeth maps not loading properly.
I had read on a separate that some people had success in getting them to work again by moving them all onto the internal drive, so I did that and they still didn't work.
It was only when I also unplugged the external drives that the maps started working again.
My best guess at the problem:
I wonder if there are some drive associations or file paths being cached that are not correctly updating when game files are moved around the hard drives*. This must be resulting in a scenario where the initial game knows that the DLC is installed, but only when you try to load a map does it not find the files in the cached location it's checking, and as a result just falls over. By unplugging the external drives it makes the cached value invalid and may be forcing the game to check the absolute file path rather than relying on a cache, which then allows it to find the correct location.
This is just a guess, could all be complete rubbish, but I know the above solution has helped solved the problem for me - would be interested to know if it does for anyone else.
* (I don't know if the xbox does any kind of automatic defragging but if it does could also potentially cause the problem for files that haven't been manually moved).