I noticed the same thing as soon as the battery got replaced it drove like it was new. Im a little confused why the cars drive-ability suffers so greatly with a under rated battery. There should be a recall on the crappy OE battery for sure.I had to go to 2 dealers before i got a new battery. First one told me nothing was wrong and to not leave my obd2 plugged in while parked. Everything worked better for a month before the heater started losing temperature again. Now i got a new battery and the car acts like a whole new 3 month old car.
The car drives like new with a proper rated battery. You are doing a disservice to the Diesel community keeping these battery s in service.
Any where there is decent cold the cars performance and drive ability suffers greatly.
Maybe a re calibration of how the alternator operates is in order as well.