OK, so the project took another turn.
I spend the last few days looking at the 2 batteries, the extended and the stock (both samsung original) and it bothered me on the question: why is the extended thicker just enough not to fit with the standard back door?
So I took the dare and what the heck, it is only 25 euros to answer the question!
So I stripped the battery!
To my surprise I discovered that I have been fooled! The extended battery could have been crafted in such a way to fit the standard door!
On the photos you will see some steps I took and I will need to find a second camera to show the end result.
When you remove the sticker you see the nfc chip.
When you remove the nfc chip there is a lip/recess were it was sitting
The lip is just tall enough as the nfc on the side plastics
The bottom plastic cap was removed and so was the top
The plastic on the bottom needed to be shaped in such a way as to follow the angle of the battery door
Magic! The battery door sits in its place and is totally flat and the angle is as it was with the stock battery!
I have the feeling that if I sand down just the little part in the middle of the door to make it flush, then I would have zero strain in the door and it would not unlatch as easy but not too much to let the battery wiggle inside it.
I will post pictures of the phone with it tomorrow.