I did indeed let it run and sure enough, it finally kicked out some more info. Unfortunately, not what one would have hoped for, however. Here's what it says now:
Running First Aid on “BlueWD” (disk3s3)
Repairing file system.
Volume is already unmounted.
Performing fsck_hfs -fy -x /dev/rdisk3s3
Checking Journaled HFS Plus volume.
Checking extents overflow file.
Checking catalog file.
Invalid node structure
Invalid sibling link
Rebuilding catalog B-tree.
Disk full error
The volume BlueWD could not be repaired.
File system check exit code is 8.
Restoring the original state found as unmounted.
File system verify or repair failed. : (-69845)
Operation failed…
So, what next? WD support says it's dead and I should just chuck it, which is certainly an option, but I hate to lose all that backup history, not to mention the cost of replacement, unless I truly have to.