UPDATE 2: Following the advice I found on a different site, it attempted a full image backup using dd (is it really that simple?):
sudo dd if=/dev/sdb of=/mybackup/PRST1.img
This resulted in the following error:
482172928 bytes (482 MB copied)
I guess at this point I really need to find out if this is a physical hardware error or not. After all, the reader is still under warranty, so in that case I should locate the blocks, tell Sony/support where they are (who are obviously not able to find out on their own), and demand replacement.
Or if it's not faulty hardware, then I should continue the path in this thread. I guess it's safe to say that I can skip another attempt to make a full image backup of my PRS-T1? So then it's probably back to the question where to get the image of a good PRS-T1...