Guys, thank you all for your kindness to help me with my problem.
Unfortunalely, I was very busy lately, and was not able to quickly respond to
all of your reactions.
The bad thing is that I was not found what I was hoping for, but at least
there are some alternatives that, if they will work, I would be happy with
them too.
The next time I make a backup, I will try some GUI frontend for dd+rsync,
testing the ones from your suggestions first, and I will also look up for
some others on the Internet.
At least I know what path should I take.