Those are my typical steps on flaked out laptops for getting data.
Between a caddie with a USB connector and some Linux live distro, I’ve done a fair amount of saving stuff for home people and a few times on the job.
I'm currently working my way through a messed up Linux Mint 17.2 update that hosed the video drivers. Linux has no undo update function. So far I loaded Mint 18 on a spare SSD to get the comouter up and running. Much is on Virtual Boxen so transferring *.vdi files should regain most functionality whilst figguring out how to fix the broken files.
I learned in 1992 that one needed to have a second comouter to be able to look stuff up to fix a "broken" primary computer.