An update: I just noticed an entry called Panel; it is found in "Application Menu > Settings" menu. Out of curiosity, I launched it, and a window appeared with various stuff, and I saw three tabs. I clicked on "Items" tab, and I saw a list of various stuff, including "Clock". I experimentally clicked the "Edit the currently selected item" button (I already selected the "Clock" entry in the list by then). I then saw the same Properties I had dealt with some days ago. I picked a time format and closed it. This time the panel clock now showed the time in desired format. The settings even persists through the rebooting.

Now, I'm happy that it is now solved on a certain level, but it is clear to me that a certain logic got broken somewhere in the interactions. I hope that in itself would be enough clues for a knowledgeable developer to figure out what went wrong with the first approach described in my original posting and fix it. Anyway, thanks for all the suggestions and advices!