Chosen Solution

The entire display assembly is loose, is there any way to disassemble it and repair this?

You could have a simple where the hinge screws have loosed up or the clutch mechanism with in the hing is worn. The process is the same. Follow this IFIXIT guide: MacBook Pro 13" Retina Display Late 2013 Display Assembly Replacement. After disconnecting the battery (Steps 1 though 6). Jump down to Step12 to gain access the uppercase side of the hinge screws. If they are not loose you’ll need to jump back to Step7 and follow the guide to the end taking the display fully off. Then carefully slide the back clutch cover to the side to gain access to the lid side screws. If these are things you need new hinges.