Are you saying you've erased two Time Machine volumes in an attempt to address this issue? I understand that you don't regard Time Machine as your main backup, but that still seems like radical surgery even if you "only ever use Time Machine to pull up previous versions of written documents,"
Yes...but the surgery isn't quite as radical as it appears.
I only just partitioned the drive a couple of weeks ago, and there wasn't much backup data to worry about. So, it wasn't like I amputated a limb, leaving a stump, but more like amputating something that wasn't much more than a stump.
Also, going back to documents is never more than a couple of weeks (once I've finished the editing, the items are usually published within the next two weeks).
I think I would have suggested resetting Time Machine on your Mac before erasing anything on any backup drives. See
Full Reset of Time Machine for details.
I did that this morning but it didn't generate any positive results. Here's the sequence after finishing the complete reset:
1. TM acknowledged that 159.43GB of 159.73GB were available.
2. TM than began calculating changes which included the exclusion (TM's decision) of more than 547,000 items.
3. TM began the backup and almost immediately said it could not complete it because it required 183.05GB but only 159.43GB were available. (Note: the drive being copied only has 85.54GB used.)
It seems more than likely that the problem resides on your Mac's drive, if the same symptoms manifest themselves when you're connecting to two different blank external volumes.
That's what I suspect (not based on any great knowledge of how these things work) and I also suspect it's related to the fact that I had the 10.6.8 Combo update done in the midst of all this.