I'll keep teasing away at this off an on.... when it stops raining!
It seems like the rain finally made it to the mainland of Europe. On the rain radar, I noticed some heavy clouds and showers coming from your direction!
What you mentioned about your spare battery isn't entirely impossible. When you first charged your battery before storing it, it will retain its charge for a long time. Only when you first load it with some reasonable load, i.e. a lamp, it will soon drop to 12.8 volts. Most DMM's have a very high input resistance, and therefore do not load the battery significantly.
The voltage raise is not uncommon either. At the end of a charge cycle, gas bubbles are formed (hydrogen). Some of this gas may have been present until you moved it. Moving the battery may have caused a slight acid strength increase, enough to cause an increase in reading during your measurement.
My own battery... it's a long story . Battery is fine for sure, though. Yesterday, I used an oscilloscope with a current and voltage probe (on the battery) to see what is going on. It is all very interesting, but very puzzling too. I think I will start a new thread with a more appropriate title, something like "things you rather wouldn't want to know about your alternator". Tomorrow I'll do some more testing near the alternator to get a better picture of the output at the alternator itself and post some screen shots.