Have the similiar problem with my UX31E (mainly poor performance of the Sandisk 256GB rather than the SSD dying) and recently upgraded to a Samsung EVO 850 M.2 with a very small adapter on eBay which fits inline with the SSD. This means there is no problems with the back cover.
I know alexandremadurell posted the link, but it's well worth checking for anyone looking at changing/upgrading: https://jure.tuta.si/?p=40
There is a lot of information there and links to the different adapters including the slim-line adapter I used.