I think the best thing to do is to copy the KNOPPIX-DATA directory, since that neatly isolates all the personal files. Just be careful: there are a lot of sneaky dot-files in there that probably shouldn't be tarred. I haven't had a chance to explore that further.

All I know is I tried to use Klaus's method and it only partially, I suspect when it hit one of the weird-looking aufs dot-files. So I tried a different tar without them (I did this by using two computers, one with the old image and one with the new one, making the old one an NFS server with /KNOPPIX-DATA exported, then copying all of it to a mount point on the computer running the new image, then copying that into my home directory as "knoppix" which prevented me from copying files that shouldn't be copied. In retrospect it probably would have worked just as well if I'd just moved the data on the old image to the old image's home directory [which would skip the problematic files], tarred it up and transferred it to the new image). But instead of using Klaus's method I used the "-b debug" cheatcodes and executed the command myself to see what would happen. There were no errors and the files were moved properly. I'll try it again with some of the problem files in the .tar and without them using Klaus's method when I have some time to spend testing.