You have your important stuff backed up as a matter of routing anyway, right?
If you don't, get free 50-GB of storage at https://mega.co.nz/ and copy it up there right now.
The vast majority of failures don't screech or smoke. They are from bad sectors on the drive, head misalignment, or contaminants like dust or smoke. When the system continually has trouble reading and writing to the drive it can predict that a failure is imminent. Running a checkdisk on the drive will detect bad sectors also.
Hard drives have had S.M.A.R.T. capability (Self-Monitoring, Analysis and Reporting Technology) for some years now, and some of the meansurements the drive takes on itself are very good predictors of impending failure.
“I don’t believe that there is any reliable way to tell a hard drive “is in imminent danger of failing” unless it’s emitting smoke or screeching like a banshee.”
This is not true. Drives today (and even 10 years ago) have/had predictive firmware that measured all sorts of parameters including temperature, variations in speed and spindle current to predict failures. some even went so fare as to analyze patterns of correctable errors to predict failures.
Better yet, go buy a terabyte drive for $70 and use USB 3 or Thunderbolt to connect the computer and drive. You can’t beat the bandwidth of a local connection.
If you are really paranoid, buy two backup drives and rotate one of them off-site, preferably to your safe deposit box.