I think I will just leave it be for the time being - or at least until I get a few spare hours.
Most of mine have all got the wrong month set. It's not even mentioned in the manual. Since they were never supposed to completely lose power (even when semi-discharged, settings are still supposed to be held even though display won't light), I don't suppose the need to set the month was ever foreseeen.
We should count ourselves lucky we can even set the day !