I am waiting for a replacement drive with which I will try to clone the drive using ddrescue as lcoughey suggested.
Just to be clear: any drive of the same or equal size is fine for cloning to, it doesn't need to be a same model or anything.
@mraikes: I'm not sure it is being recognized (at least not consistently). It's possible a drive could fail during cloning, but when you clone from sector 0 to last sector, the heads are moving smoothly from one end to the other. Recovering files and connecting to a OS means the heads will be jumping all around the drive, which is much more risky.
Also, when we clone a drive, especially if the drive is very bad, we'll target the important files first (but still in such a way where it starts at the first sectors on the drive and moves to the end in a straight line -- not jumping all around the drive). I don't believe it's possible to "target-clone" without a DDI or equivalent.
There really shouldn't be any "thrashing" when cloning a drive (at least not for long if you're doing it right). The idea is to recover all the good (non-thrashing) sectors first, quickly, and easily. Then you go back and try the bad sections.
Even for just one file, I believe a full clone is safer, if you can't "target clone," (it's VERY rare that we have a drive fail when cloning, like less than .01%, although we are probably cloning using tools which make things "safer" for the drive than something like ddrescue; disabling parts of the firmware and experience helps too of course

).
Not every data recovery event requires heroic measures.
True, but I would counter that the
SAFEST recovery does require such measures.