If you add "after", the first two will still be adverbial. 1. might change to an adverbial of time rather than manner. 2. might change to an adverbial of time rather than causation/reason.
In 3, you are adding "after being", not just "after", converting it into another adverbial phrase - perhaps of time, though it's difficult to imagine another time at which he could have spent most of his life there. So, I wouldn't change it.