As a lot of the electronics are Merc stuff I wonder if they suffer from the same voltage instability problems? I've driven plenty of cars which I couldn't turn off due to a completely dead battery but they were admittedly ancient fossils I've always assumed that they ran completely off the alternator when the engine is running. Makes me think that the cure of a replacement battery may well work but not actually be the total cause of the electrical gremlins. Having said that I'll be off to get a fresh one the minute it plays up
I'll stop now wouldn't want to upset anyone else