With all due respect I think the observation you are making is very much looking for a pattern that's not there.
It didn't completely surprise me that the battery drops to 12.2 under load just before a start, there's a lot of heavy circuits kick in, but once the engine is turning voltages should recover very quickly as the alternator comes in so I wouldn't expect any symptoms of a weak battery to hang over into full engine on unless the battery was so bad it's barely starting the car at all.
If you had a bad map sensor its own reading would be nonsensical, so go look at that before considering it as a fault.
...if it creaks, it's probably made by VAG