Update on these issues, for those interested: the drag and drop copy process did eventually complete, about 30 hours! Then I started another TM backup, and it seems to have processed an amazing number of items (but this could have been because of an incomplete prior backup in the copy), and eventually completed after 22 hours. Then I proceeded to reformat my original backup disk (to remove partitioning that was limiting the backup size) and copy the "new" backup to the original disk. This time, I did it by a "block copy" ("restore") process using Disk Utility, and it only took 2 hours (150 GB). Much better! It also copied the name of the disk, but this was easily fixed by a "normal" name change procedure in the Info box.
I then did a SW update and fix permissions, and am trying another TM backup. I'll report when this finishes. At the moment, it is "preparing" and is up to 32,000 items!