Well, my problem went away. Backups are once again completing successfully.
But a bit of playing might have fixed that.
I have a 2nd unused 250GB drive in the system, so I thought since I cannot have automatic backups for now that I would set up Windows 7's built-in software RAID-1. After that, for a full day I perceived degraded performance, and Disk Management was in a persistent state of 'synchronizing' disks. This made me grumpy, so I decided to undo the mirror.
Windows would not let me remove the mirror from 'DISK2', only 'DISK0', I thought, 'what the hell, I have backups, let Windows have its way'.
So now with my system drive moved to a different physical disk (I checked the past 2 days) backups have been doing their thing.
I know that sometimes there is not a truly single fault or point of failure. It's frustrating when I fix PCs fora living, but then cannot figure out my own problems :/
I am considering my issue resolved.