I don’t think you’re gonna have any luck swapping boards / cases / enclosures etc.
If it was that easy for anyone to access encrypted data … then what’s the point of encryption at all?
You might have more luck with Linux Tools to open the encrypted drive to view the files and recover them.
The links below are for My Book … you may get lucky if it works for My Book Live.
Last Resort … a data recovery service, if the files are very important (cus, it will cost you)