But if you already knew the drive was damaged, why push it to the point when you can't possibly have the time to image it, which will take forever? Feels like advising somebody to push through their asthma until they're about to lose consciousness.

This. I naively thought that SpinRite could "fix" the bad sectors (forcing the drive controller to copy the data to a spare sector) and let me copy out of the data through a normal process after, but bad sectors are often an indicator of a larger mechanical issue.