"Is persistant system freezing and "typing lag" sign of a failing hard drive? I have done everything I can think of just short of asking to see if it would be possible to get a Genius Bar appointment. (The freezing is new.... Is that a sign of any kind?)"
You have a NON-retina 2012 MacBook Pro, is this right?
Chances are, the internal ribbon cable (that connects the internal drive to the motherboard) is failing. This is a common problem on the 2012 design MacBook Pro.
When the cable gets flaky, "good communication" between the drive and the motherboard is lost. Things slow down or won't work at all. It looks like the drive has gone bad, but it's "just the cable". Replace it and things go back to normal.
The replacement cable is not expensive.
It's easily installed.
The Apple genius bar may be able to diagnose this for you, BUT... they may not be willing to do the repair any more (yes, I know that sounds infuriating).
If that's the case, you can fix it yourself with a Phillips #00 driver and the replacement cable.
You can go to ifixit.com to see what's involved:
1. Take back cover off
2. Lift out drive and disconnect cable
3. Carefully disconnect cable from motherboard, plug new cable in
4. Re-connect to drive and then put the back on.
But if you're going to do that (or have it done for you), it would be a good idea to put an SSD inside. It will make the MBP "feel like new" again.
You could then take the old drive (that was inside), and use that for a backup drive.
I would use CarbonCopyCloner or SuperDuper to create the backup (both are free to download and use for 30 days), and forget about Time Machine.