. . . you should backup your filesystems to image files on another device. Use dd conv-noerror.
It would be nice to split the 65GB HD into a couple 32 GB compressed images, to fit on 32 GB thumb drives.
That might be an approach for a simple routine backup, but rather useless when trying to rescue data from an erroneous filesystem or device as appears possible in your case.
To the contrary, if you image your filesystem(s), to preserve optimal chances of being able to rescue data, you should not operate in read-write mode on the image per se, but only on a
copy of the image.